If this is truly 1957 as stated (and I have no reason to doubt it), then this is two years before Burnett got her first major break in the Broadway musical Once Upon a Mattress, although she had done some television work beforehand. This is ten years before her immortal self-titled show would hit as a series. And I can't quite tell, frankly, how parts of her routine are going over with the audience. I'm wondering if they knew what to do with her, frankly. But I think it's great. Hints of the mayhem that was to come.
Update: Alas, the full clip has been taken down, but this snippet is still up with a Burnett intro now. If anybody finds the full thing, please let me know. And, well, at least we get confirmation that it's 1957 now.
Update Again: Now that clip has been taken down--and her comedy routine has been replaced with a classic song of hers.