Do Pets Reincarnate?

I used to have the pleasure of "babysitting" a golden retriever named "Shadow" when pudd'n was a baby. Pudd'n took to Shadow like a duck to water. We lived next door to a lovely English lady named Maggie and she in turn would baby sit pudd'n for us. Shadow was a big red golden and Pudd'n LOVED her. He'd crawl all over her and they'd share dog biscuits. Jack loved Shadow too, although she was too over weight to wrestle about the house. But they would hang out none the less and loved to go for walks together.
Shadow passed away 3 years ago. It broke our hearts, she was the first dog to that pudd'n loved. She was gentle & kind.
I've been noticing lately that Samwise has a lot of similar traits that Shadow possessed. Are these just traits that all goldens have? Or did we get lucky in the wheel of karma and we've got our beloved Shadow back? I've never owned a golden before, so I'm not sure. I know when the day comes and I have to get a new Aussie dog, I will know that they will all be hyper as shit until they at least reach 11 years old. They all like to heard and they are smart & loyal.
Some of the traits of Samwise/Shadow that I have noticed:

1. "hops" up & down when you get food dish ready

2. Voracious eater

3. Will go and lay in puddles of water or sit in the middle of yard with sprinklers on

4. Always sits down when you brush him. No matter how many times you pull his butt up and tell him "stand", he sits.

5. Most important, he loves Pudd'n.

I don't know if these few traits qualify for reincarnation. Sam is still young and it will be fun to see how his personality unfolds. I'll have to get Maggie over here to see what she thinks. She already thinks "I'm daft" with out having to bring this up. ;)