The short answer is: We don’t know if there will be animals in the afterlife.
The longer answer is: There is something we can know. Unlike humans, who have spiritual souls, we know that animals have material souls that cease to exist when they die. Does this mean that you won’t see Rover again in heaven? That’s something else we can’t know. If he chose to do so, God could certainly re-create our furry friends along with the rest of the universe (cf. CCC 1048). A couple of answers I’ve heard to this question, often asked by grieving children, are:
If we need animals in heaven to be perfectly happy, they’ll be there. (What is left unspoken is that we only need God in heaven to be perfectly happy.)
Rosalind Moss, in her Evangelical Protestant years, liked to say, “Well, if Rover asked Jesus into his heart as Lord and Savior, then yes!” (What is left unspoken is that an animal can’t do that.)
For good discussions of the possibility of animals in the afterlife, see Peter Kreeft’s *Everything You Ever Wanted to Know About Heaven… but Never Dreamed of Asking * and Anthony DeStefano’s A Travel Guide to Heaven.