Bunny Rabbit must have been a male cross-dresser.
That’s just it, the glasses made Bunny look female, but the actions were more like a male. I’m 68 and I still don’t know!.................
Wikipedia refers to the character as MR. Bunny Rabbit:
https://en.wikipedia.org/wiki/Captain_Kangaroo
Cosmo Allegretti appeared as Mr. Bunny Rabbit and Mr. Moose (both of which he also created), Dennis the Apprentice, Willy, Miss Frog, Mr. Whispers, Dancing Bear, Grandfather Clock, and Uncle Ralph; he was the voice of Aniforms puppet TV Fred (a live-action on-screen puppet that appeared behind the blackboard in the Treasure House), and was the artist behind the Magic Drawing Board[6][7]