There seems to be much dispute as to the meanings behind nursery rhymes. The general consensus regarding 'Pussycat, pussycat' seems to be that it may refer to an actual event and a cat owned by a member of Queen Elizabeth the First's household. There also seems to be a Scottish version that possibly refers to the relationship between Elizabeth and Mary Queen of Scots....
Poussie, poussie, baudrons, where hae ye been?
I've been to London, seeing the Queen.
Poussie, poussie, baudrons, what got ye there?
I got a guid fat mousikie, rinning up a stair.
Poussie, poussie, baudrons, what did ye do wi't?
I put it in my meal-poke, to eat it to my bread.