Hi, Goodbye Mog, by Judith Kerr is the book 3littlefrogs is referring to. Badger's Friends is another book about death.
I'd just tell her. I shouldn't think she'll be that bothered, but will look sad as that's what she'll think you want to see. I think it's a bad idea to say he's gone to live somewhere else - she might worry that if she got ill you'd send her away.
Our cat died 2 months ago. I told my 7 year old (at end of school day) and she said, with sad face, "oh, how sad....... it's (my best friend)'s birthday in 10 days".
We had a funeral, buried him in a box with a few flowers and photos of the girls, planted an apple tree over him (we'd been meaning to plant it out for ages). Sang "Peter Perkins, he's a jolly nice cat" and talked about nice things Felix did.... afterwards my 2 year old said, "oh, I wish (othercat) was dead too"... so perhaps the funeral was too much fun?!
I think from what you say, your problem is that like me, you are upset, which is fine. It gets better. I don't burst into tears whenever they talk about him, I just smile now. Well, I well up a little!