It was an Amanda Show or All That skit where Amanda Bynes or Lisa Foiles is a tiny little girl in a house and the skits would often feature her opening the door or the windows and there was something looking at her through the window, one skit had a black and white rabbit.
Sounds like the wake up scenes from All That. Here’s a YouTube video of some of them (including rabbit) but can’t seem to find more with a quick search.
https://youtu.be/U_Xb1DTf42g