I'm not sure whether that's the RIGHT way to go...

You know your parents better than any of us do. Some are VERY supportive from day one. Some are supportive after education. And, some not supportive at all. You've heard all of this here, I know.

From the way you described things - you may still be a minor (that is - your access to doctors is "through" your parents). In this case, getting to the gender specialist would require the support of at least one of them. (If you are NOT a minor your options are different.)

So - assuming you're a minor and need your parents help to get to the doc, it's important to get their support early on. Several ways you can do this include thinking about where they've stood on various LGBT issues - in your experience. (Even parents who are anti most LGBT issues can be supportive, when the person in question is their child... And some who are supportive in the generic have problems when it's their child.)

One thing I would suggest strongly - is not just telling them how you've diagnosed yourself but more tell them that you've felt questions and have done a LOT of research on the internet on your own... And while you think you know what's going on you need to work with an objective specialist to make sure and see what's really going on. And while doing this, you need to be asking for their help and support. You can point them to some of the online resources you've found, and tell them you've been talking to your GP about things too, and that HE thinks you should talk to a specialist (even if you're the one that asked for it, your GP wouldn't have referred you if he'd not thought it was the right thing to do). This takes SOME of the onus away from you, and points out to them that you've been mature and your doctor agrees that you need to look at things further.

If you're not a minor, then seeing the specialist BEFORE you talk to your parents may well be the right thing (as Sephrena indicates - the specialist can help facilitate or at least guide you in the discussion).

So, it all depends. As a minor, it's to your benefit to do all you can to help get your parents supportive.

One thing to keep in mind - more and more people today have had experience in meeting a TS person. I have one young friend (through my church) who has worried about coming out to ___ parents (pronoun intentionally blanked)... However, since I'm friends with ___ parents, when ___ does they'll already have had a positive experience interacting with a TS person.

Best wishes.
Annette