I was under the impression that you should take a very young baby to the dr if they seem ill.
I agree about the wet nappies and feeding being ok, but to me four weeks is very young if they are vomitting because of a bug.

Mind you, I'm more inclined than not to take my kids to see a dr ... a few times I thought they were ok but they had ear/chest infections and needed anti-biotics, and similarly when they didn't seem well it was nothing more than a "post-nasal drip" that time would heal.

Use your instinct - if you "think" you should take her, then take her. Your peace of mind is just as important.
Hope J is better soon.