Remmington makes a youth model. 7. It comes in a few good calibers, .243 and .260 are the 2 best. Short stock and light weight would work well for you. My wife is 5" 1" and my boys model 7 in .260 fits her well.

Not sure I agree with a .243 being to small. A few of my hand loading good ole boys out here in hill country would sure aruge about .243 being to small. . .they have dropped many a deer using .243 90gr hand loads.