I actually believe that God will probably have some animals in Heaven, and might even raise back to life some of the animals that human beings were close to in life. There's certainly nothing preventing Him for doing so anyway. God created animals in the first place because they represented some aspect of the perfection of His creation, and so the reconstituted earth presumably would not be lacking whatever prefection of creation they represented
Yes, I think some saints have postulated (I could be wrong; it's been a long time) that at the end of time, after the General Judgement, that God will "renew the earth" (which is referenced in the Apocalypse) and the entire planet will be like the Garden of Eden. Thus, those that are saved will have the ability to visit all of earth's wonders and the animals there will be docile, friendly and loving.
Imagine the story of the Cure of Ars, where he denied himself even the simple pleasure of looking upon the new technology of the railroad. Or imagine some cloistered nun in France, who never got to see the Eiffel Tower (due to her penance of joining the monastery). Wouldn't God make it possible for such saints to experience such worldly pleasures in eternity, after they gave up such for the Glory of God? Surely, God would make such possible.
Even the idea of visiting a certain period in time...i.e. to see how the pyramids were built, to see the famous battles of christianity, to see Charlemagne crowned king...such matters are human concerns, but they do provide some human pleasure, and how would God, the author of Time itself, not provide that to those that are faithful to Him?
And, in a far lesser miracle, I think God would make it possible for those animal lovers to see their 'long lost pets' or even to make friends with 'new pets' on the new, renewed earth. Eternity is a LONG time. And God would reward sensible creatures (i.e. humanity) with such sensible pleasures, in addition to heaven's spiritual heights.