I think I missed the quote that said that animals had immortality prior to Adam.
Remember, Jesus physically resurrected, thus conquering literal physical death (If He had only conquered a spiritual fall He would not have physically resurrected differing us from Angels). This is one reason He chose to become a physical man and why our inheritance is higher than the Angels.
Luk 24:39-40
39 Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have.
40 And when he had thus spoken, he shewed them [his] hands and [his] feet.
Hbr 1:4 Being made so much better than the angels, as he hath by inheritance obtained a more excellent name than they.
Hbr 9:15 And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions [that were] under the first testament, they which are called might receive the promise of eternal inheritance.
1Pe 1:4 To an inheritance incorruptible, and undefiled, and that fadeth not away, reserved in heaven for you,
It is all there for the diligent student to be rewarded.