I am a transwoman so my experiences may be completely different to that of someone who was born female and wishes to transition to male. That being said, I thought I'd share my thoughts anyway because I have been through this and thought it might be helpful for the OP to get a trans perspective.
First of all, I am glad you have made an appointment with the GP and are willing to discuss counselling. That's the first step out of the way. Whilst you are at the GP, I really would recommend pushing for that counselling referral before doing anything else. I would hold off doing anything physical for now, so no breast binders and defiantly no puberty blockers.
Just take your time with this and make sure your daughter attends those counselling sessions. Hopefully she will open up to the counsellor and will be able to be honest about why she feels this way, why she wants to be a boy and how she thinks this will help her.
In the meantime just support her. If she asks you to call her 'him' and asks you to call her by a specific masculine name then go along with it. Also make sure she knows she can talk to you about anything and that you will support her no matter what.
I agree with other posters here that there isn't much that can (or should) be done at this stage other than wait and see. She might decide in a few years time that she is happy with being female and that she isn't trans. That is fine. Alternatively, she might come to the conclusion that she will be better off transitioning in which case support her if that is the decision she makes and make sure she knows you will support her if she chooses to go down the path.
Whatever you do though, please don't lie to her and tell her she can change sex because that's just cruel. If I had been told I could change sex as a teenager I would have been crushed when I found out it wasn't possible and I dread to think what I would have done. Luckily my parents were supportive and didn't lie to me.
I disagree with the posters who say that transitioning early is the best thing to do. It wouldn't have been the best thing for me and it wouldn't have been the best thing for other trans people I know. Unless those posters are talking about socially transitioning rather than physical transitioning of course. The former is okay if that's what helps the person suffering from gender dysphoria but physical transitioning is a definite no no. As far as I can see, nobody is objecting to the OP's daughter socially transitioning.
I socially transitioned as a teenager and became known as 'she' and by my feminine name but I didn't start physically transitioning until later. After I had grown up, matured, been given guidance and counselling to help me make sure I was making the right decision. Gender reassignment is one of the biggest life changes you can make and it's not something that should be taken lightly or something that someone should feel pressured into doing.
When I was a teenager I hated going to my counselling sessions. I hated my body and I hated the fact I couldn't get gender reassignment right there and then. I hated the fact that I couldn't start changing my body straight away and if I had been offered puberty blockers then I would have jumped at the chance.
However looking back as an adult I can see that puberty blockers would not have been right for me at the time. Looking back I'm glad that I couldn't start physically transitioning and that my parents made me attend counselling because it helped me get my head straight and helped me figure out whether all of this was what would help me. So I don't agree that a teenage automatically has it all figured out and knows what's best and what they want.
There's nothing much for the OP to do at this stage other than keep the dialogue open and make sure her daughter knows she is there for her.