I have a cousin whose wife is about the size of the OP. She uses a 7mm-08 and has tipped over several elk in CO including a really nice 5x5. I don't know of any of the elk she has shot that needed a second bullet. But she also lives in elk country, has the entire season to hunt and can be patient in waiting for the right shot angle.

Another good cartridge to consider that many people forget about is the 6.5x55 Swedish. Great round, low recoil and performs great on game. You can get good lightweight rifles in either chambering. I'd suggest you go to a shop with a big selection (Cabelas etc...) and handle as many different brands and styles that you can and choose what feels good for you. The Ruger compacts may be just the ticket.