Well, I know some children's book writers who have gotten published, even if they had to go the personal route of self publishing. I've seen some fine self-published children's books!
If you don't have an agent, and you are out there looking on your own for a publisher, I highly recommend the latest edition of "Jeff Herman's Guide to Book Publishers, Editors, & Literary Agents." Get your ducks in a row, and then make contact with the agents/publishers if you intend to go the traditional route. If not, study the companies who offer self-publishing packages including the artwork if your book will be illustrated (of course the majority ARE.)
If writing is your passion, you will stick with it no matter how many rejection slips you get. Have fun with them, wallpaper a wall in your office with them, and when you get published and your book is selling well, walk to that "rejection wall,"