Q:

Can we use "whisky" to describe a squirrel going up a tree?

I am confused that the term "whisky" is used in the poem The Squirrel to describe a squirrel going up a tree (though 'whisky' denotes a drink). According to the Cambridge Dictionary, "whisky" denotes:

NOUN
B2 a strong, pale brown alcoholic drink, originally from Scotland and Ireland, made from grain such as barley, maize, or rye

But confusingly, this word (whisky) is used in the following poem:

The Squirrel (Anonymous)
Whisky, frisky,
Hippity hop;
Up he goes
To the tree top!
Whirly, twirly,
  Round and round,
  Down he scampers
  To the ground.
Furly, curly
  What a tail!
  Tall as a feather
  Broad as a sail!
Where's his supper?
  In the shell,
  Snappity, crackity,
  Out it fell.

Please pardon me, if I am mistaking the poem.

A:

It’s a rare word (or expression since it collocates as “whisky frisky”), but it is in the Oxford English Dictionary (OED.com) so it’s not a neologism. It’s a poem, so the author likely isn’t worried about using a rare word. In any case the meaning is clear. It is defined as:

Light and lively, flighty.

And it was used as far back as 1782:

Talking in such a whisky frisky manner that nobody can understand him.

Cecilia
I also think I found another example here. 
Also here in quotes. 
And again here (although it might be a reference to alcohol, I’m not sure). 
And yet again here. 

A:

Interestingly, the expression “whisky-frisky”, spelled with a hyphen, is an example of a reduplication, albeit very rare. Similar to  binomial pairs, reduplication is usually two words but which rhyme together, e.g. hoity-toity,  jeepers-creepers, pitter patter, and topsy-turvy. In the English language, whisky-frisky stood for someone drunk on whisk(e)y and probably unsteady on their legs, so quite the opposite of a sprinting squirrel!
The author of the book History, meaning and the sheer joy of words, Vivian Cook, says it is of American origin and is virtually obsolete. She also lists other examples that are mostly forgotten: kitch-witch, holums-jolums, and hitherum-ditherum, note the hyphen that joins the two words together, this is missing from the poem cited by the OP.
However, the poem The Squirrel is filled with reduplicative  expressions that small children find particularly appealing due to their quirkiness and rhythmical beats. 

Hippity hop (nowadays hoppity-hop)
Whirly twirly
Furly curly
Snappity crackity

EL&U has many questions and answers dedicated to this fascinating linguistic phenomenon, I would warmly recommend the OP to delve into its archives.  
https://english.stackexchange.com/search?tab=votes&q=reduplication

A:

As other answers have pointed out, this particular example of rhyming repetition dates back at least as far as the 18th century, being used in "The Race," a satirical poem by Cuthbert Shaw (1766), who considered it one of his "favourite words" (see footnote).

Prove then, oh Goddess! to my labours kind,
  And let the sons of Dulness lag behind,
  While hoity-toity, whisky-frisky49, I
  On ballad-wings spring forth to victory.'
49A favourite word of this author. See Education, a poem.

It was also used in volume three of Cecilia, a book in five volumes by Frances Burney (1782), and in a rhyming chorus in "The Highland Reel," a 1788 farce by John O'Keeffe.

Whiskey, frisky,
  Prancing, dancing,
  Sorrow kick to Nick the De'el,
  Care or trouble who can feel,
  Lilting up the Highland Reel.

The "Whisky Frisky" poem itself appears in an 1871 children's book, Little-Folk Songs, by Alexina B. White.

In that early version, there was a fifth stanza that is missing from most later versions of the poem:

Stir the fire,
      Put on the pot,
  Here's his supper
      Hissing hot!    

Around the previous turn of the century, the poem was included in a children's reading primer series, The Culture Readers: Embodying the natural method in reading, by Ellen E. Kenyon-Warner, Pd.D. (Doctor of Pedagogy), in a volume aimed at the "second half year".

This "natural method" involves the child reading texts of interest and performing targeted study of words encountered in their reading.

The "Whisky Frisky" poem is presented with a list of related vocabulary words, some of which appear in the poem and others of which are related through rhyme or similar spelling lessons (e.g. silent A in read, lead, bead).

