Yes, I firmly believe in eternal life for both people and animals.
In fact, there is a ghost cat living with us. I'll hear a cat scratching in one of the litter boxes but when I go in to look, no cat is there. All four of mine will be asleep in a different room so I know it's not them.

I've also had "experiences" when I worked at our Fort here that's haunted. Plus my Dad stopped by for a visit the morning after he passed on.