Is it possible to safely keep a rodent?

I have a large dog, who is a pitbull/husky mix. She has a high prey drive, and is very rambunctious. She doesn't come into my bedroom, and if she does, it's because i have food, and she is focused on that. Her prey drive is high, and she chases rabbits and other rodents in our backyard, as well as deer. I have been wanting to get a smaller animal, like a rodent (hamster, mouse, hedgehog, rat) something that can be kept in my room, and only in my room. I'm afraid though, that if i get another animal, it wouldn't be fair for either animal. The dog i had previously was very relaxed, and my hamsters didn't seem to mind her. I haven't had a pet other than my new dog since, so i don't know how she will react. If she is aggressive towards the animal, it's wouldn't be fair to force the animal to live in fear. She would be able to smell the animal, and would likely be interested in my room, and enter more often. Is there a way to train out her prey drive? Can i safely keep a pet if i keep it in my room and away from her (very much out of reach)? or would that be a bad idea, and i should wait to get another pet. She's very young, being 3 years old. Is a prey drive something she will age out of? I want to be 100% sure both animals are living happily and comfortably, and it would make me upset if i accidentally mistreated one.