Most children's writers will need a literary agent, yes, and do bear in mind that there are agents who specialise in handling work for children, so it's these you'll need to appeal to in due course. The one exception is that if you're writing picture books, you can go direct to publishers ... though on the whole our advice is still to get an agent, at least while you're still getting to know the industry.
No! Publishers will commission their own illustrations and would much prefer it if you present them with the text alone. The one exception: if you are a pro illustrator already and have written words to your own pictures.