I tried this a couple of years ago. Based on what I read, the children's book publishers absolutely prefer to use their own illustrators. Check out:
http://www.amazon.com/2006-Childrens-Writers-Illustrators-Market/dp/1582974020
Lots of good information there. Once you start researching the market you find out how many children's books are written vs how few get published. Sad, but true. I refined my story a lot before sending it out. I got a lot of impartial opinions along the way then sent it to quite a few carefully targeted publishers. All were returned with form letters from the publishers that read something like, "We receive 20K submissions/year and publish 15 titles."