It depends on your goal. If all you want is a few copies of a book to hand out to your friends, self-publishing isn’t a bad option, but if you do this, I urge you to visit the forums at Absolute Writeand check them out before you do business with them. Many of them have very, very bad reputations and deservedly so.
If your goal is to write a book that people will want to buy, I suggest you go to a bookstore or library and find books that are similar to yours and look at who published them. Look at the names of the illustrators and find some names of illustrators you like. Do some research and find out where they are located. Maybe you can find some near where you live. Contact some and see if they are interested in your project.
Read How Real Publishing Works. Read Children’s Writer’s & Artist’s Online Toolkit.
ETA: I like jjimm’s suggestion about a series, with seahorse, etc.