These thoughts are based on my own experience and opinions, so you must also consider the views of others who are much better known in the field of Children's Book Illustration.
Agency representation is a very personal choice on the part of the illustrator or author/illustrator. Just as you go about carefully choosing the agent you most want to represent you, the agent will have criteria for acceptance of illustrators and authors.
If you are just beginning to write and/or illustrate for children a great agent could give you a head start. But devoting too much time to finding an agent shouldn't be a priority. The best pathway to success is to keep your writing and your illustrating fresh, explore new ideas, work hard on any assignment that you receive and take the suggestions and criticisms of editors, designers, and art directors with grace and act upon them. Focus on your work and make it the best you can. Attend conferences, workshops, and classes that will help you grow as an artist.
So, for the sake of an example, let us say you found a great agent, the agent agrees to represent you and find suitable assignments for your type or art. You now have someone or a group that will handle the contracts, negotiations, and submissions to houses that only accept them from agents.
You will need to be prepared to accept the assignments given to you. You can't be too choosy about the work that your agent offers you. You will be asked to share in the promotional costs. In addition you will need to let go of the business issues that are the responsibility of the agency. You will need to meet deadlines, take criticism, make changes and behave in a totally professional manner. An upbeat and positive attitude are great qualities in an author or illustrator and are appreciated by the publishing community .
Your talent, if your nurture it, will create a pathway for you with or without an agent. Be the best you can, be excellent.