Don't worry about getting a good handgun "for a girl'; just get a good handgun for YOU. If you've tried the 9mm M&P Compact and liked it, I don't know any reason why it should be considered a bad choice. Go for it!
I would, however, HIGHLY suggest a special-made holster-purse, or a holster secured to the inside of your existing purse. A holster has several purposes which are important; first, it keeps the weapon in exactly the same place and at the same angle, so if you need it in a hurry, you know exactly where to go to find it and grab it, even in the dark. Second, it protects the gun from bumps, impacts, and getting tangled-up with other objects. If you just drop a loaded M&P in your purse, it's not a matter of IF you will have an accidental/negligent discharge, it's a matter of WHEN. For instance, you toss your purse on the car seat and the cell phone bumps the pistol's safety off; you grab the purse and one of your car keys pokes into the trigger guard; then one more bump and BANG!, someone gets hurt/killed. Even putting the gun in its own compartment in the purse will not prevent this type of problem, and it certainly won't prevent it from turning upside-down (the slide is heavier than the frame, so it will end up at the bottom, eventually; same thing happens when people carry a gun loose in a coat pocket).
Hope the above info has been helpful. I do not wish to discourage you from buying/carrying, but I don't want to read about your accidental shooting in the newspaper, either.
"Placement is power" -- seen in an article by Stephen A. Camp
(RIP, Mr. Camp; you will be remembered, and missed)