"Dwell on the beauty if life. Watch the stars and see yourself running with them" -Marcus Aurelius If there is more beauty in seeing your beloved pet in heaven, why not?
I won't worry too much what the Bible says or not - re animals (It doesn't address your question as it is not the Bible's function.) Since it doesn't speak to the question why not create your own beautiful reality beliefs on the question? Life is hard enough and the unconditional love is the joy that lights our way. Animals are so good at this. Forming our own empowering beliefs, those based in beauty, truth, goodness and love can ease our path is this dark world.
"I wish I knew no astronomy when the stars appear"...sometimes a man needs a dream to make things bearable. Me and my critters will lay in the warm sun and soft grass forever and ever, and if not I'd soon just rot. Reason and logic be damned. Who's to say?