No. The animal has no immortal soul. It dissolves at death: "ashes to ashes and dust to dust". There is nothing of the animal that can endure once the body is dead: therefore, it is impossible.
It is possible that an animal could be recreated by God, or even conjured out of one's own memory - I see no reason why it should, however, or why one would desire such. I am in agreement with those who has posted in other threads of this topic, to the effect of, "what an insult is it to God, that one feels one can not be happy with the beatific vision, but must have Rover there too, as if a dog could augment God!"
If all people are to live in harmony in the New Jerusalem, assuming that not only animalophiles can be saved, some feel equally so that a place containing dogs or cats could not be paradisaical, disregarding any philosophical arguments one way or the other - which would seem to militate that one group or the other would be changed by force to enter heaven (abrogating free will, that is, if the beatific vision isn't great enough that it can't survive without the enhancement offered by Fido), that people who don't adore animals can't be saved (heresy), that animalophiles can't be saved (see above), or that heaven is separate and distinct for each and every individual (see above).