I *do* think God could do this. If He's all powerful, of course He can do this. But I agree with others - it's not how He seems to work. He might be able to, but He doesn't seem to do it (I don't know of anyone that had that prayer answered without also utilizing people He's gifted on earth).
I'd also add that I doubt God is as hung up on sex organs as humans are. I think there's more to being a man or a woman than the organs (that said, I'm not discounting the importance of our bodies matching who we are). I won't speak for you, other than to say He very well may have made you a woman when He made you. You might not need to "turn into" a woman, although you may feel the desire and need to live as you are, conforming to who He created you to be - which very well might be a woman. There's nothing wrong with living an honest life, even if your birth certificate doesn't list the truth. You shouldn't live a lie just because some humans looked at the outward and, thus, came to the wrong conclusion (there's a whole spiritual lesson in this - it's yet one more way we focus on what we can see rather than what actually is).
God can answer our prayers in many ways. We get in trouble when we assume that He must do things a certain way. He's helped me meet my financial needs, for instance, by giving me the ability to learn in my field, get hired by an employer, etc. It took hard work on my part, but the ability to do that came from God. It's no less God's work than if I received an anonymous gift of cash on my doorstep! I thank God for it, just like I thank Him for my "daily bread" which I bought with income I received as a result of the time I spent laboring for my employer. That doesn't mean God still isn't 100% the source of everything. I am extremely thankful for how God can help people become who they are through gifted doctors and surgeons. I wouldn't deny that these abilities came from God, nor would I ignore accepting any gift God offered me, even when my own work and the hard work of others may have been part of how God accomplished it.
So maybe He has answered your prayer. Maybe it's not that you will wake up, having done nothing different the night before, with the body that is true to yourself. Maybe instead it is that He will guide you and help you on the journey to becoming true to yourself and showing the world God's truth in you.
As for our bodies being proper, that's going to happen for sure. Just not always on earth, sometimes in heaven. But regardless, that doesn't mean we can't live true to ourselves on earth, through whatever means God provides. If that includes things like clothes that reflect our being or even things like surgery, we shouldn't deny ourselves those options - particularly if they allow us to be honest with ourselves and others.
