Is there a copyright on the use of Whats Up Doc for commercial purposes?

Answer 1

Not sure about the copyright, but the last person who attempted to register a similar trademark in the US Trademark Office (related to restaurant services) wound up in litigation for over two years when Warner Brothers found out about it and ended up abandoning the application.

Probably not, because slogans are not normally subject to copyright protection.

However, it is a distinctive trademark slogan of a famous cartoon character, and almost any commercial use of the slogan that conflicts with the owner's rights is likely to result in unpleasantness.