I think that it is possible that we get strictly theological answers from the sources of the Tradition (Sacraments, Scripture, Liturgies, Creeds, Ecumenical Councils, Fathers, etc). I know the Catholic Tradition uses philosophy a lot, but I wouldn’t consider this even a source of the Tradition (if I had to though, I would consider it one of the lowest sources, with the possibility to be overruled by higher sources such as the Sacraments and Scripture). That is because it’s non-theological. All philosophy stems from the understand that the world is rational and that we have the capacity to know it. In accordance to this understanding, philosophy is the logical investigation of causes, and one does not necessarily need God to do this (though St. Thomas Aquinas Christianized Aristotelianism pretty well). But theology is the divinely revealed understanding.
I’m just gonna throw out some ideas, but, before I do so, I just wanted to say that it is possible to argue that those passages from Isaiah describing “the wolf lying with the lamb” and such are all fulfilled in Christ’s Incarnation, Eucharistic death and resurrection, and the Church after this. Animals, within the prophets, especially unclean wild animals, usually are symbolic of the gentiles. To say that the “wolf would lie down with the lamb” probably means that gentiles and Jews will have covenant unity in the New Covenant. The proof is from the visions of Daniel. All of the terrifying beasts he sees represent gentile world powers. Same with Peter’s vision in Acts.
Now in regards to the question of whether it is possible that animals will be in the New Heavens and Earth, since this is the climax of the New Covenant, it must be said that within every previous covenant, animals were always considered to be in covenant with mankind. Consider the Noachic Covenant, as well as the fact that, within the Mosaic one, animals too had to share in the penance of the Israelites on the Day of Atonement. One could argue, however, that man is in covenant with animals because of the fact that all of the covenants, prior to the New, were covenants made while being in the deathly reality of fallen Adamic original sin, which animals represent. My personal interpretation of Genesis 1-3 would view Genesis 2-3 linearly proceeding Genesis 1 in time (Genesis 1 being only a prologue of simultaneous good and bad news…the result of God reordering the world after Adam’s sin within a flood similar to that of Noah, the proto-Noachic flood), and the original “animals” of Genesis 2 actually being angelic creatures (Jewish Tradition, for example, considers some angelic creatures to be serpent-like; consider also Ezekiel’s heavenly chariot visions where he sees apparently animalistic angels). Therein, God made animals only as signs of life to the dismay of the deathly presence of evil, underneath the authority of man. But, nonetheless, there is a message that mankind is in covenant with animals, and surely, this must teach us something in regards to the New Covenant (though I believe we shouldn’t just throw the Old Testament upon the New without properly eschatologizing it first, if necessary).
Also, concerning the Temple of God on earth, a type of the True Temple in Heaven, it is stated that “even the sparrow finds a nest” therein, specifically on “the altars of the Lord.” There are also ideas within Jewish Tradition that part of the belief in sacrificing animals was to “send the animal to where you wished to go” (the burnt animal rising in the smoke to the heavens as a sign of your own longing to go to heaven). Is it possible, according to this within the Tradition, to argue for a belief in animals within heaven? Also, one of the Cappodocian Fathers (one of the Gregorys, I believe) stated that he couldn’t imagine heaven without his beloved dog. But this can be overruled, being an extremely low source of the Tradition.
I think the answer actually lies in our Sacramental, Christological, and Trinitarian theology, especially in regards to theosis. If Christ empowers us to become human persons with the divine nature WITHIN a Divine Person (check out this idea within my post entitled “Eucharist, Trinity, Holy Spirit, Temple, Body of Christ, Theosis idea”), and he promised us, within the Gospel of John, the ability to do even greater mighty deeds than he did, then, surely, we should have the power to complete the work of Christ, in general, and to raise up many aspects of our still fallen world, including animals, through our relationships with them. Wouldn’t the fish that the resurrected Christ ate be the most heavenly, blessed fish that ever existed? Does it still exist within Christ?
This is just a few starting points that I’ll bring to the table.