Publishers, especially in the US, prefer to match authors and illustrators themselves. In fact, most will automatically reject anything that comes with an illustrator.

I'd suggest you join www.scbwi.org

They're very helpful with both basic information (your question about illustration, or things like do you have to copyright your ms. before sending it to a publisher) as well as advanced stuff for once you're published (sample contracts for speaking at schools, etc.)

Plus very nice people. Lots of local shop talk groups and peer critique groups and etc.

And lots of the latest publishing information on who is or isn't looking.

Even for unpublished writers, belonging to SCBWI is a help in approaching publishers since it shows you're taking your children's book writing seriously.