I love my furry tail waggin' best friend and he loves me no matter what. He comes to work with me every day and he is a uniting force in our office and on the job sites I visit each day. I know well from past experience the pain you speak of when a pet dies and I really took that into consideration when getting my current dog. In the end, I decided that although giving my heart over to another pet will ultimately result in a big sadness down the road, it is better to have experienced the good years with him and the joy of providing a happy life for him, than to have missed out on all that just because I wanted to sheild myself from experiencing future sadness.
The thing I have to remember about animals is not to project my own feelings onto them. They are not sentimental like we are, they pretty much live in the moment and accept things at face value. They don't reflect on the big picture meaning behind everything they experience and perhaps that's why we enjoy them so much. It wouldn't be much fun to have a pet that worried about the future or whether or not there was an afterlife, held grudges or moped over things in the past or was always looking for ulterior motives. Sounds like your little poodle had a good life with you and you both enjoyed eachother and you have to be thankful for that even though it wasn't for as long as you'd hoped.
Time will be a friend to you in your loss and in time you'll adjust maybe even to the point of maybe wanting to give another animal a good home and a good life.