First, life is life, you eat something, it has to die for you to absorb the nutrients to sustain yourself. Second, Genesis at least does not make mention as to whether or not animals died before Adam sinned. The only thing specific is that Adam brought death unto himself and his seed. Where the bible omits things that we have questions about (and Genesis is very short, very basic, a lot of fastforward and begats, a lot omitted), you have to look to God's creation itself and try to piece together the best answers you can.
There are a lot of forms of life, and remember, man was created last, so these life forms were created before men, that are carnivores, parasites, carrion feeders, and things like fungus and bacteria that break down and decay dead things. Humans didn't die before sin, that part is NOT omitted from Genesis. But animal death is not clearly stated one way or the other, so animals dying and feeding on each other can still be a part of the plan, and is absolutely necessary for population control in a balanced ecosystem. God said "be fruitful and multiply". The world would be absolutely overrun if you had insects breeding but never dying. Some species entire reproductive strategies involve reproducing by the hundreds or more, anticipating most of the young will die but a few will survive to breed in the future. In biology we call this the R strategy, reproduce frequently in high numbers hoping that some survive but with minimal investment in each one. The adults tend to have short lifespans as well, so it's necessary (and designed this way) for them to reproduce a lot to keep their numbers up.
Humans are what biologists call k strategists, few offspring, HIGH investment in each one, longer lifespan (or in humans case originally intended to be immortal)
God creating things that breed literally more frequently and in higher numbers but rabbits but never die, this planet is too small for that. Note that when we're reborn in new creation, there won't be marriage anymore, and by extension, no sex or children, so the population control won't be a factor, at least not for humans. Again, revelations isn't very clear about animals, that's mostly omitted. There's some stuff pertaining to Christ's 1000 year rule before creation is remade, with the wolf and the lamb lying down next to each other to suggest there won't be predator and prey relationships anymore. But that's about it.