Awesome. Then the GIC should be fine for you. Just make sure everything is moving along properly, keep up with your GP, make sure he/she is getting it all set up right. At first my GP said he would do something but never did, it took an extra 6 months. My GP at the time was incompetent though.
For what it is worth, even if I could not afford it, I would prob save up for the surgeries to be done private.
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Anyway to go into specifics, for me it was like this.
1) GP -> refers to generaly psych.
1 month
2) Psych makes sure you are not a mental.
3)GP refers to GIC (he didn't do it for 6 months)
Should take about 6 months (for me a year).
4) Have an appointment at GIC, tell them you want hormones. -> Generally will tell you you need to be full time and name changing and living as chosen gender blah blah (maybe less strict now).
6 months (if very lucky you don't have to wait)
5) Go back for next appointment, if you are satisfying their conditions they will prescribe.
This is for an adult since I was 23 when I finally got to the GIC. I do not know the rules for minors, I imagine they may be a little more hesitant. Hopefully you are almost 18?
Either way it took at least a year when I was at the GIC to get prescribed.
PS legally changing your name is super super easy and pretty cheap. Make sure you get it done before going to the GIC. It will be a good idea since they put a lot of stock in it.