I'm not completely sure animals have consciousness, although I think it's likely they do, and, if they don't, we don't need to worry about them. So it seems like we should try to look into that before we look into helping them directly.

I think it's worth pointing out that requiring absolute certainty before we care about animal welfare sets an unreasonably high bar. This standard implies that animals should be treated as non-conscious until definitively proven otherwise, which is a highly questionable position given the current scientific consensus.

We humans are animals, and given the evolutionary continuity and the similarities in brain structure and function between humans and many non-human species, it would actually be quite surprising if other animals weren’t conscious. The burden of proof should rest on those claiming that animals lack consciousness, not the other way around.

Both the Cambridge Declaration on Consciousness (2012) and the New York Declaration on Animal Consciousness (2024) reflect this view. The Cambridge Declaration states unequivocally:

“The weight of evidence indicates that humans are not unique in possessing the neurological substrates that generate consciousness. Non-human animals, including all mammals and birds, and many other creatures, including octopuses, also possess these neurological substrates.”

The New York Declaration reaffirms and extends this, concluding that:

“First, there is strong scientific support for attributions of conscious experience to other mammals and to birds.

Second, the empirical evidence indicates at least a realistic possibility of conscious experience in all vertebrates (including reptiles, amphibians, and fishes) and many invertebrates (including, at minimum, cephalopod mollusks, decapod crustaceans, and insects).”

Given all this, delaying action until we reach 100% certainty is both morally and scientifically unjustified.

I'm not so sure that the total amount and aggregation of "happiness" would be increased if the baby is saved.
It's probably true that saving the baby would generate more happiness, because they will be happy for more time than the adult would have been. 
However, I think it's also true that allowing the adult to perish could result in significantly more suffering due to all the people that have a personal relationship with them.
I also think that avoiding suffering is much more important then creating happiness. So, while I'm happy to create happiness, I am hesitant to trade the expected average happiness of a future person for the suffering of all the adult's friends and relatives.