A lot will depend on how much JRT your puppy is made up of. They have a reputation for being quite predatory so, you will have to make sure her interest is focused on something rather than living things. With my Lara who is a shorty JRT (she'll be 2 in December) it is toys, particularly tennis balls.
My Lara couldn't care less about birds and squirrels outside as long as she has her ball. I actually contacted her breeder, wondering why she lacked the usual JRT instincts (not that I'm complaining.) She told me that the rest of her siblings are "typical jacks" and that even cats aren't safe with them around. I have a cat and they are the best of friends!
My border collie Bailey who is a gentle soul had a hand in raising her so, maybe she taught her that being predatory was not acceptable? I really don't know. Jacks are extremely focused dogs. If you can get her to use her predatory instincts on toys, your other animals should be safe. However, don't EVER leave them alone until you're absolutely sure that she won't go after other living things.
BTW, what is she crossed with?
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