If you don't have time to update your passport, then your documents only need to match. They won't ask for your driver's license, they'll ask for your passport. Your ticket and passport must match exactly. Book the ticket in your birth name and gender and you should be fine. The only possible glitch is if you've changed a lot since your picture. If you really dramatically look different from your picture, they could ask for additional ID. At which point you would need something with your birth name and a current photo. But honestly, I think it's pretty rare. The advantage you would have here is that everyone will speak English and you can probably explain why you look different. I travel on a female passport and get sir'd right up until I hand over my passport, sometimes no one bats an eye, sometimes they look a little closer and then let me go. If you're on T, I'd try and dress as female as you think you can handle for the time in the airport and then go back to your normal self after. For what it's worth, I normally go back to being sir'd on the airplane even though my name is female on the manifest.
I hate to have to say this, but if you are a race that tends to be profiled by either your home country or the one you are traveling to, you may have more scrutiny.
