You may be "petite" but women generally have longer legs than men - you've seen 5'2 men riding, so can you. The area you may have trouble with is upper body strength; often men are more muscular through the chest and arms and have longer torsos so if the bike starts to tip they have a better chance of holding it up. This means that the weight of the bike, and it's centre of gravity will be a factor for you. Provided you can sit on it with both feet touching the ground I would highly recomend the honda cbr 125 or, failing that, the kawasaki ninja 250. The bike manufacturers are slowly waking up to the fact that women ride too, and that not everyone wants the fastest bike with the most horsepower. Scooters and smaller displacement bikes are selling in higher volumes. Even motorcycle riders are getting fuel efficiency conscious and this means more choice for us.
Go sit on some bikes. Talk to some dealers. Ask for recomendations from local riders, clubs or training groups but recognise that for many, motorcycles are about passion, and that means a lot of unsubstantiated opinions ;-) Many dealers have both new and used stock. Some people buy smaller displacement bikes and upgrade once their interest in biking is confirmed and their confidence increases. This means gently used bikes on the market. Unfortunately, at least in my end of town (Ottawa, Canada) they hold the value very well and don't come down in price much at all. Before you buy, get insurance quotes from a variety of companies, in writing. They shouldn't vary too much since they are usually based on engine size and value, but you'll likely get a much better reception if you also insure your home and car with them. Many places will give you an insurance break if you take a training course, and raise your deductable.
BTW, I'm close to 6 feet so I don't have your petite issues - but I've been teaching motorcycle training courses for a long time now and have put a lot of shorter women through the program.
Good luck with that 'convince the mom' thing. I would never have ridden if it weren't for my dad riding - it would have been hypocritical to say no to me :) Now that I'm a parent I don't know how my mother could handle me walking out the door with my helmet and keys. Why ride? Biking gives you a sense of adventure and exploration. It makes you a little different from other people. Makes you a little more independant and allows you to see things in new ways. I can't be sure she'd buy any of that...
Good luck, have fun and be safe.
And of course, take a training course :-)