Well, to be sure, the Bible is not a literal text. In 1400 BC roughly when someone composed the book Genesis, they did not literally mean the universe took six of our days, they mean six time units of an indeterminate length. At that time, the world did not even have a uniform calendar to go by to even agree on the dates.
That said, does the Bible not say we are given dominion over all creatures on the Earth, and is it not replete with stories of sacrificing lambs, goats and other things? Not that it matters. It is no skin off my nose how or what you eat.
Some would tell you they take care of the deer and other animals by culling their excess, so that those that remain don't starve in the winter.
I take the bible differently than you. But that's OK. That's actually a whole other discussion. Maybe one we can have another time and place.
And yes, we were given dominion. But the whole idea of dominion has been massively misunderstood by most Christians, I truly believe that.
God is our example. God is selfless. I mean, look at Jesus, he laid down His life for us, out of love.
So God wants US (well, at least those who follow God, but I think He also wants mankind in general to do this) to take care of the animals in the way that HE intended, which we know from His original and ultimate design. And that is with love, mercy, and living in peace and harmony. Just like in the pre-fall world (Eden) which was God's intent, and like it will be again, according to the Bible, when Jesus returns.
Here's a picture of that future... the new Earth:
The wolf will live with the lamb,
and the leopard will lie down with the goat.
The calf, the young lion, and the fatling will be together,
and a child will lead them.
The cow and the bear will graze,
their young ones will lie down together,
and the lion will eat straw like the ox.
An infant will play beside the cobra’s pit,
and a toddler will put his hand into a snake’s den.
None will harm or destroy another
on My entire holy mountain,
for the land will be as full
of the knowledge of the Lord
as the sea is filled with water.
Isaiah 11:6-9
And here's a little reel I made about that passage:
(It doesn't embed properly here, so it's best to watch it full screen)