I believe there are two types of artists. The ones that like to be involved in all matters, that are somewhat extroverts, don't mind handling fees and asking for higher pay. That can keep track of clients when not paying on time and that don't mind handling contracts. And then there are artists that just want to draw. I'm in this group. :o)
I am very bad at negotiating and contract terms etc, so for me an agent makes perfect sense. I don't mind sharing a percentage with them because they truly earn it doing all those things I don't want to do. But if you think you can handle these things on your own then you can certainly be without an agent.
Children's illustrators can find jobs on their own without agents, no problem. Make sure you advertise on portfolio sites and send promotional postcards regularly. Of course, always have your work online on your personal website and make sure your portfolio is appropriate for children's books.
One thing that is important to know is this, if you are an illustrator and don't have any intention of writing and want representation, you might want to look for an artist rep and not an agent. Reps handle the educational market which is the bread and butter these days. So you could be busier doing ed work on a daily bases. Art reps usually take a higher percentage than literary agents, around 25 to 30%, so you have to take that in mind as well. Literary agents usually focus only on trade and it's a slower process, but they take around 15% cut.
Whatever you decide to do, make sure to take your time choosing and agent/rep. Ask a lot of questions, they like this and expect it too. The agent-client relationship is a close and important one. You want to feel comfortable with your agent or rep and hopefully have a long lasting career together.