Most of the time, the illustrator has other work to finish first, before they can start on your book, so it is not at all uncommon for a picture book to wait two or three years, before it is actually in print. Oh, and just in case you were wondering, beginning writers have no say in who illustrates their books. Many books are rejected again and again before they are published, if ever. My two easy readers were rejected 27 times before they sold. You have to have a healthy dose of perseverance and stubbornness to survive the writing business.
Rejections are a part of the business.
Learn to roll with them and don't take them personally. Pick yourself up and start over again. The more you write, the better you write. How I write is just that, the way I write. If you find some ideas that you can use, great.