Awww, Jilly. So sorry for your loss
it is hard when your children are so little, my daughter was 5 when one of our cats met the same fate, and it helped her to be part of the "funeral", I don't think I will ever forget her coming inside to get her toy drum so she could play him a song, and drew him a picture to go in the box with him. She and my DH went outside to do the burial - she didn't see the body coz it wasn't very nice, but she knew he was in there. She stood for ages, solemnly drumming away, DH didn't want to disrupt her because it was obviously important to her, but she just kept on drumming and drumming and drumming, and then turned to DH and said all solemnly "Is it ok to stop drumming now?"
At 3, I wouldn't expect a little one to really grasp the concept at all. The book is a great idea, but don't worry too much if she seems very matter of fact about it, or doesn't get it, little ones are very resilient. Just answer any questions she has as honestly as you can, within what you think she can handle, and that's all you can do.
hugs to you all, it's a horrible thing to go through. Xxx