Agreed. I think too many people try to make sense out of the senseless. Sure, it would be more convenient if JA shot first, but 1) No one but JA really knows what happened in that bathroom, 2) Do we really expect a borderline personality to take sensible action while killing her ex-boyfriend in a rage? 3) Knives are more "personal" and are often the weapon of choice when it comes to revenge-style killings.
Why JA brought a gun to a knife fight I'll never know, but I would pose that it was a back-up. Turns out she didn't need the gun after all, so she shot him at the end to add insult to injury.