If I had a transgender kid, then I would be fully supportive of them, because all I'd want for, well, anyone really, not just my own flesh and blood, is for them to be happy and comfortable with themselves, as long as this doesn't involve illegal activities.
However, this does not mean I'd allow them to jump immediately into hormones and surgeries, because the majority of people who regret doing these things are people that never saw any professionals, or only saw one for a short time, so I'd make sure my kid understands all of the options available for them to avoid that kind of scenario. I also understand that transgendered people can start hormones from the age of 16 in the UK, however, I'd probably prefer that they wait until they're about 20, so that they know they're not being influenced by hormones from puberty any more (as for some teenagers who come out as trans, it is just a phase). Of course, this does not mean that I won't do everything I can to make them feel comfortable until then.