For fiction, whether you’re writing for adults or for children, it always makes sense not only to finish your book, but to revise it. Get some readers (not just your mum and dad), and redraft and redraft until you feel you have got it to absolutely the best point you can without help from an agent and/or publisher.
No author’s first draft ever gets published – and an agent wants to really get the sense that you are hard-working, have spent a lot of time with your manuscript and you are determined to get it right.
For non-fiction, you need a proposal that gives an overview of the project, a breakdown of the chapters you plan to write and at least one complete chapter to give a sense of your voice and direction.
For all writers I would work on your ‘back of the book’ pitch – a couple of hundred words that really crystallises what the book is about. I far prefer these to long synopses.