Kingdom of Knuffel

You have a baby tiger

A dolphin!

I'm going with a peacock, either regular or albino

You have a giant constrictor boa

Your familiar's a graceful crane.

your familiar is a scarab

Your familiar is a very clever fox.

your familiar is a stingray

Umm, you need something that won't be phased by all those drapes....
Something small and nimble.
Something...
Hm.

Okay, your familiar is a tiny little tree shrew.
That'll be an utterly adorable critter who can just climb right up those gauzy curtains without being phased at all!

I think your familiar's a flying squirrel.