I found it rather easy too, but I think I was lucky to be in touch with the right people. It is variable in NZ.
My counsellor, who I had been seeing for about a year as I went through a process of coming out and exploring, refered me to an endo at my request. I said "I want hormones" and she said "sure, see this guy, here is a letter". So I did. It took about 2 months to get an appointment, he asked I get some bloods before I go. I saw him and he asked me "what do you want to happen?" I told him and tadaa here was a script for hormones. Easy. The hard bit for me was making the decision to reach for them.
I then went to my doctor and he asked me "are you happy with the treatment you have", I said "yes" and that was it. He gives me repeats as I need it no problemo.
I saw a psyc 3 times for my letter. That was kind of easy too. I just talked about myself for a few hours and he was satisfied I met the criteria. He had conversations with my counsellor too as they are collegues, which helped speed things along.
I'm pretty happy with how supportive the medical people I have been in touch with have been. They can be pretty accomodating if you just ask what you need in my country. Like I decided I needed to get antidepressants, went to the doctor, told him what I thought. He concurred. Very un-gate keeper like people. Almost like "I trust you know what you need, and I can see no evidence to suggest otherwise, here you go"