shorter people do not
need a shorter rod. bad misconception. so you are right on this one. savor the moment. these are rare enough in life: when you get to be right and your woman has to accept being wrong.
also, i agree that a fast rod is a big mistake for a beginner. so you are two for two!
now, she probably has small hands if she's only 5' tall. and that is an issue you should
consider. there are some women's rods with reduced size grips. and expert lady casting instructors like carolyn parker and char bloom will tell you this really makes a difference. (both ladies are also petite, orvis-endorsed, and joan wulff casting instructor school grads)
my wife and i did a TON of research and field testing of women's fly rods and equipment a couple of years ago. and our top pick close to your price range is the elkhorn ladies line
. admittedly, it's probably $100 more than you mentioned for the rod and a repsectable reel and good line, but it is worth it to do it right if she really wants to fly fish. it's a progressive taper med-fast rod that is more medium than fast when compared to say a tfo pro series or echo or redington crosswater. it's about x2 the cost of the redington crosswater, about $50 (max) less than the tfo, and about the same as the echo at around $200.