Well I'd say no because humans are special. We were given souls, we worship God. Pets just like a planet or a rock or a water drop are temporal things. Here for our pleasure in this life. Once we are in heaven there will be no need for these temporal things because we will be happy already. In heaven there is no fear, depression, sadness...etc. Hence no pets will be needed.
As someone else said its our emotional tie to pets that makes us refuse to accept they won't be in heaven. Sort of like shock after a tragic event happens. Many stay in denial for a long time. Lets face it, the cat I spent 20 years with and loved with my whole heart, its to hard to accept I won't see them again. But its a reality I must face and have accepted.
The worry I have in these kind of topics is how many essentially make their pet an idol. And then how many say essentially God isn't loving if their pet isn't there. In heaven we are there to worship God, not our pets, not even our family/spouse.
The truth is that there is no clear answer either way about animals in heaven. Or at least in the case of pets. So we won't know until we get there. As much as I loved my cat, I'd gladly never see her again if it meant I could see Jesus instead. Anyways Jesus died on a cross for humans sin, not pets or anything else. But to each their own, I do realize people have a hard time accepting they won't see their pets again, but if it comforts them in thinking they will. Then thats ok. Whatever makes you feel happy.
Though obviously the second we die and see heaven, we won't say "I don't see my pet!" because we won't have that kind of emotion to think about. In other words we won't even be caring about a pet because it will no longer be important as on earth it was just an emotional attachment.
---edit---
I do remember when both of my cats died last year everyone sent me poems and pictures about the "rainbow bridge" and while they meant well, it was sort of offensive at the same time. Having accepted I won't see them again, having someone tell me I will just made me upset. I am not one to live in denial. Also you can get into then what about the rest of the animals that aren't pets? Do they get into heaven? If not why?