How Old Should the Udhiyah Be?
Question

Is there a specific age for the sacrificial animal? Is it permissible to slaughter a cow as a sacrifice when it is one and a half years old?
Praise be to Allah.Can you slaughter animals that are younger than the recommended age?
The scholars (may Allah have mercy on them) agree that Islam has prescribed the age for sacrificial animals and it is not permissible to slaughter animals that are younger than that. Whoever slaughters an animal that is younger than that, it does not count as a sacrifice. (See al-Majmu’ by al-Nawawi, 1/176) 
For example, al-Bukhari (5556) and Muslim (1961) narrated that al-Bara ibn ‘Azib (may Allah have mercy on him) said: A maternal uncle of mine whose name was Abu Burdah slaughtered his sacrifice before the prayer, and the Messenger of Allah (peace and blessings of Allah be upon him) said to him: “Your sheep is a sheep for meat (i.e., not a sacrifice).” He said: “O Messenger of Allah, I have a young goat (according to another report: I have a young she-goat) (according to a report by al-Bukhari (5563): I have a jadha’ah which is better than two musinnahs – shall I sacrifice it?)” The Prophet (peace and blessings of Allah be upon him) said: “Sacrifice it, but that will not be valid for anyone but you.” According to another report, “It will not count for anyone after you.” Then he said: “Whoever slaughters (the animal) before the prayer has slaughtered it for himself, and whoever slaughters it after the prayer has offered the sacrifice and followed the way of the Muslims.” 
This hadith indicates that a jadha’ah of goats (young goat) is not sufficient as a sacrifice. We will explain below what jadha’ah means. 
Ibn al-Qayyim said in Tahdhib al-Sunan: 
“The phrase “It will not count for anyone after you” is a definitive statement that it would not count for anyone after him.”
Muslim (1963) narrated that Jabir (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “Do not slaughter anything but a musinnah, unless it is too hard for you, in which case you should slaughter a young sheep (jadha’ah min al-dan). 
This hadith also clearly states that only a musinnah can be slaughtered, except in the case of sheep, where a jadha’ah may be offered. 
Al-Nawawi said in Sharh Muslim: 
“The scholars said:   
A musinnah is a thaniyyah of anything, camel, cow or sheep, or anything over that age. This clearly indicates that it is not permissible to slaughter a jadha’ah of any animal in any circumstances, except sheep.” 
Al-Hafiz said in al-Talkhis, 4/285: 
“The apparent meaning of the hadith suggests that a jadha’ah of sheep is not permissible except if one cannot find a musinnah. Scholarly consensus says something different, so this hadith should be understood as referring to what is better. So it is mustahabb not to slaughter anything but a musinnah.”
Al-Nawawi said the same in Sharh Muslim. 
It says in ‘Awn al-Ma’bud: 
“This interpretation is the one which is correct.”
Then he quoted some of the hadiths which indicate that it is permissible to offer a jadha’ah of sheep as a sacrifice, such as the hadith of ‘Uqbah ibn ‘Amir (may Allah be pleased with him) who said: “We slaughtered a jadha’ah of sheep with the Messenger of Allah (peace and blessings of Allah be upon him).” Narrated by al-Nasai, 4382. al-Hafiz said: Its isnad is qawiy (strong). It was classed as sahih by al-Albani in Sahih al-Nasai. 
It says in al-Maws’ah al-Fiqhiyyah (5/83) concerning the conditions of udhiyah : 
“The second condition is that it should have reached the age of sacrifice , by being a thaniyyah or older in the case of camels, cows and goats, and jadha’ah or older in the case of sheep. A sacrifice does not count if the animal is younger than a thaniyyah except in the case of sheep, or if it is sheep that is younger than a jadha’ah…. The jurists agreed upon this condition, but they differed as to what is meant by thaniyyah and jadha’ah.”
Ibn ‘Abd al-Barr (may Allah have mercy on him) said: 
“I do not know of any dissent with the view that a jadha’ah of goats or anything else that is offered as a sacrifice apart from sheep is not permissible. Rather it is permissible to sacrifice a thaniyyah or anything older than of all of these. It is permissible to sacrifice a jadha’ah of sheep according to the Sunnah.” (Tartib al-Tamhid, 10/267. 
Al-Nawawi said in al-Majmu’ (8/366): 
“The ummah is agreed that with regard to camels, cows and goats, nothing will do except a thaniyyah, and with regard to sheep, nothing will do but a jadha’ah, and that these are all acceptable. But some of our companions narrated that Ibn ‘Umar and al-Zuhri said: A jadha’ah of sheep does not count. It was narrated from ‘Ata and al-‘Awza’i that a jadha’ah of camels, cows, goats and sheep does count.”
Recommended age of sacrificial animal
With regard to the stipulated age of sacrificial animals, the scholars differed concerning that. 
A jadha’ah of sheep is a sheep that has reached the age of six months, according to the Hanafis and Hanbalis. According to the Malikis and Shafi’is it is a sheep that has reached the age of one year. 
The musinnah (or thaniyyah) of goats is one that has reached the age of one year according to the Hanafis, Malikis and Hanbalis. According to the Shafi`is, it is one that has reached the age of two years. 
The musinnah of cows is one that has reached the age of two years according to the Hanafis, Shafi’is and Hanbalis; according to the Malikis it is one that has reached the age of three years. 
The musinnah of camels is one that has reached the age of five years according to the Hanafis, Malikis, Shafi'is and Hanbalis. 
(See Badai’ al-Sanai’, 5/70; al-Bahr al-Raiq, 8/202; al-Taj wa’l-Iklil, 4/363; Sharh Mukhtasar Khalil, 3/34; al-Majmu’, 8/365; al-Mughni, 13/368) 
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said in Ahkam al-Udhiyah: 
“The thaniyyah of camels is one that has reached the age of five years. The thaniyyah of cows is one that has reached the age of two years. The thaniyyah of sheep is one that has reached the age of one year. The jadha’ah is one that has reached the age of half a year. It is not acceptable to offer anything younger than a thaniyyah in the case of camels, cows and goats, or anything younger than a jadha’ah in the case of sheep.” 
It says in Fatawa al-Lajnah al-Daimah (11/377): 
“The shar’i evidence indicates that a sheep that has reached the age of six months may count as a sacrifice, as may a goat that has reached the age of one year, a cow that has reached the age of two years, and a camel that has reached the age of five years.  Anything younger than that does not count as a hadiy or udhiyah . This is what the Quran refers to when it says (interpretation of the meaning): “sacrifice a Hady (animal, i.e. a sheep, a cow, or a camel) such as you can afford” [al-Baqarah 2:196], because the texts of the Quran and Sunnah explain one another.” 
Al-Kasani said in Badai’ al-Sanai’ (5/70): 
“These ages, as defined in Shari`ah, are minimum ages, not maximum ages. Sacrificing an animal that is younger than that is not permitted, but if an animal that is older than that is sacrificed, it is permitted and is better. It is not permitted to sacrifice a lamb, kid (young goat), calf or young camel, because the ages of animals that we have mentioned were narrated in shari’ah and these were not mentioned among them.’
So it is clear that slaughtering a cow that is younger than two years old will not count as a sacrifice according to any of the imams. 
And Allah knows best.