Sorry this is really long.
Hello Kristia,
Austria is a nice country from what I know of it. The mountains are fantastic and Vienna is a nice city with great shopping

Aside from that, I don't really know any particulars about the system there. While the EU is attempting to unify the system, the EU moves very slowly, and I fear that we will all be old women before we see and real progress. That link that Emily posted will likely be more helpful than anything I can say.
That said, I think the best place to start is likely going to be research. I assume you don't have your official diagnosis yet and a script for HRT (though I could be wrong). So, the first thing you should look into is trying to find out who your gatekeeper is. You did mention the obgyn, but are they able to diagnosis you or just give you the prescription and monitor your progress? For me, my gatekeeper was a Sexologist. He interviewed me and did a bunch of strange medical tests. In the end he gave me a referral to a clinical psychologist. The clinical psychologist gave me my diagnosis then passed me back to a different sexologist who will direct my transition. I think it is different for everyone here, but for me it took about 3 months from my first appointment to getting my prescription.
Another thing to consider is financing. For example, will you be covered under the national insurance scheme or your country's (not sure if you are coming from Canada). Is there an option to go through a private clinic or will you be required to use the public system. Also, you should look to find out what is covered and what is not. I am very lucky that I have lived in the Czech Republic for many years and have permanent residency here. I am fully covered under the Czech medical insurance plan and almost everything is paid for here. There is a co-pay for estrogen, but it is not a lot (I think 2 and a half months cost me less than 10 Canadian dollars). T-blockers are covered fully by the public insurance. So are my doctor's visits (well, I pay 2 dollars), SRS, voice surgery, if I want it, and the tracheal shave, if I am willing to wait a long time to get it.
One more thing to think about before you arrive here is where you fit legally into the system. Your legal rights and obligations as well as all the strange hoops you will need to jump through to get your paper work changed will depend a lot on you residency status – tourist, short-term resident, long-term resident, permanent resident, citizen. This is really very complicated and I cannot really advise you on it, but I can tell you that the best place to start is the embassy, then maybe a lawyer. I am a permanent resident here so I mostly need to follow Czech procedures for everything. However, my sexologist told me I am also the first Canadian to get treatment here and one of the first westerners, so no one really knows what to do with me. On a local level, I find a lot depends on how low-level civil servants feel that day. For example, the name change alone is really complicated and no one actually knows if I can change my name to an English one or if I need to have a Czech name at this time, if I will be allowed to have a middle name, etc. Additionally, I have not been able to get an answer about the gender marker change. In the Czech Republic the gender is only changed after SRS. However, I was born in Ontario and they will change the gender marker whenever I want provided I can give them a statement from a therapist who is legally allowed to practice in Canada. Seems like it would be simple, but no one knows if the Czech insurance will pay for my SRS if I am legally considered to be a woman already.
Well, I hope this was helpful. As I said, please feel free to ask me anything. I am happy to help you if I can.
Talk to you later.
Hi Emily,
Thanks for posting that link – it was very interesting. Sorry to hear things are so regressive where you are. I really cannot complain too much about the Czech system – though I think that most of the time it really depends on who you talk to and when. The law here regarding the treatment of trans* people was written in the 60s and it has never been updated. So, it has largely been left to individual doctors to decide what you need to do and when. For example, my first doctor refused to give my hormones until I divorced my wife. I changed doctors after that, and have had no problems with that, though the second doctor is pressuring my to go full time immediately. I have been postponing it (I at least want to make sure my facial hair is under control first) but I can tell he is starting to get irritated with me.
have a nice day,
Mary