The Queen appears at the end of the Bird & Elephant level once you've completed the level previously AND rolled up the King of all Cosmos. See that solution for additional information:
Like the King, she is REALLY big. You'll need to be about 3000m to be able to roll her up.
Here is a video of my run through the level in As Large as Possible mode where I rolled them both up:
A few notes:
1) Per Jamone the Afro in a comment on the King solution, this can be done in Eternal Mode which is unlocked after completing the level in As Large as Possible and As Fast as Possible.
2) If you bounce the Queen because you aren't large enough to roll her up directly, she will wake up and run away after several seconds so be prepared to roll her up ASAP.