‘Umrah on the part of a child who has not reached the age of discernment
Question

                I am intending to perform ‘Umrah, by Allah’s leave. My husband will be with me along with my three children, all of whom are below the age of four years. I hope that you can explain how they should enter ihram, perform the rituals and exit ihram. Is it preferable in their case to shave the head or to cut their hair?
Praise be to Allah.
    Hajj and ‘Umrah are valid on the part of children who have 
    reached the age of discernment and those who have not reached that age, 
    according to the majority of scholars; in fact it was narrated that there 
    was consensus on this point. 

    With regard to ‘Umrah on the part of a child who has not 
    reached the age of discernment, i.e. a child who is below the age of seven, 
    his guardian should form the intention on his part, after dressing him in 
    ihram garments and keeping him away from things that are forbidden whilst in 
    ihram. He should form the intention that the child has entered ihram. 

    Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:

    He should enter ihram on his behalf, i.e., form the intention 
    that this child has entered the state of ihram. He should not form the 
    intention that he has entered ihram on behalf of the child, because this is 
    not correct. Rather he should form the intention that this child has entered 
    the state of ihram. If he does that, the child has entered ihram.

    End quote from Sharh al-Kaafi by Shaykh Ibn ‘Uthaymeen 
    (may Allah have mercy on him). 

    Similarly, he should also form the intention of tawaaf 
    (circumambulation of the Ka ‘bah) and sa‘i (going between as-Safa and 
    al-Marwah) on the child’s behalf. He may carry the child during these two 
    rituals. If he does carry him, then it is preferable for him to do tawaaf on 
    his own behalf and then on behalf of the child, but if he does one tawaaf it 
    is sufficient for both of them, according to the correct scholarly view. 

    Shaykh Ibn Baaz (may Allah have mercy on him) said: if the 
    one who is carrying another person intends tawaaf on his own behalf and on 
    behalf of the one whom he is carrying, and if he intends sa‘i on his own 
    behalf and on behalf of the one whom he is carrying, that is acceptable 
    according to the more correct of the two scholarly opinions, because the 
    Prophet (blessings and peace of Allah be upon him) did not instruct the 
    woman who asked him about Hajj of a child to do tawaaf for him on his own. 
    If that had been obligatory, he (blessings and peace of Allah be upon him) 
    would have said so.

    End quote from Majmoo‘ Fataawa ash-Shaykh Ibn Baaz, 
    5/257 

    Shaykh Ibn Jibreen was asked about that and he said: As ihram 
    for a child is valid, the guardian is responsible for him. So he should 
    dress him in the ihram garments, form the intention of ihram for him, form 
    the intention of the rituals on his behalf, recite the Talbiyah on his 
    behalf, and hold his hand during tawaaf and sa‘i. If the child is incapable, 
    such as one who is very small or is still breastfeeding, there is nothing 
    wrong with carrying him, and one tawaaf is sufficient for both the one who 
    carries and the one who is carried, according to the correct opinion. If the 
    child does anything that is forbidden whilst in ihram out of ignorance, such 
    as wearing a fitted garment or covering his head, he does not have to offer 
    any fidyah because he did not do it intentionally. If he did do it 
    intentionally, such as needing to wear regular clothes because of being cold 
    and so on, then his guardian should offer the fidyah on his behalf.

    End quote from Fataawa Islamiyyah, 2/182 

    Once the child has done tawaaf and sa‘i, there remains the 
    issue of shaving the head or cutting the hair. Shaving is preferable, 
    because the Prophet (blessings and peace of Allah be upon him) offered 
    supplication three times for those who shaved their heads and one for those 
    who cut their hair. Narrated by Muslim, 1303. But if he is afraid that the 
    child may be affected by cold and the like, then it is sufficient to cut the 
    hair, but hair must be taken from all parts of the head, as is the view of 
    Malik and Ahmad (may Allah have mercy on them both). 

    See also the answer to question no.
    36847

    And Allah knows best.