If I had a child and they were to come out as transgender, I think I'd be immensely proud with them for being so brave. As an LGBT person myself, I know how difficult it can be to try and hide your identity, so I have a lot of respect for anybody else who is LGBT to pluck up the courage and come out. Regardless of whether my son or daughter was 3 or 23, I would definitely do whatever I can to make them feel 100% comfortable with themselves.
I have to admit, I would feel very concerned for them; I would worry a lot about their dysphoria and potential to become a victim to bullying and ignorant remarks. So I would do whatever I can to protect them and make them know that no matter what, I'd always love them and be there for them, and would back their decisions all the way. Regardless of their gender or sexual orientation, I know that deep down, they are still my child, with the same personality I always knew and loved and will continue to do so.