The cartoon version available via YouTube is a "YouTube Poop" version, meaning a parody made by redubbing and re-editing a video, in this case a Warner Bros. cartoon starring Bugs Bunny. I doubt the original cartoon had the same name.
"Noice" is a representation of a pronunciation of the old Brooklyn accent in which the er and oi sounds were merged, as explained in this Wikipedia article. Bugs Bunny had a combination Bronx/Brooklyn accent. The word he had in mind was "nurse." (He was talking to a mad scientist who was experimenting on him and had him laying in a hospital bed.) Watch his hands when he first says it--he mimics the form of a woman.