Hi 9snr6! First of all welcome to the forum, and have a rabbit!
I'm glad that you found the people of this community helpful to you. It's because of people like you, who have been doubting and struggling with Islam, that I think these conversations that are had here are so important.
Firstly, I think you should not have a particular sense of expectation when it comes to leaving Islam, and the separating or distancing oneself from it. The act of doing so will end up giving you new perspective and appreciate different opportunities, but this comes with time, and undoubtedly a bit of struggle. I'm glad you have a plan to move to a freer country, but as you said, this will take time to enact.
In the meantime, I think it is important for you to try to settle yourself in whatever way you can. This moment for you is one of both challenge and change, and those bring with them emotional turmoil. It can be frustrating to be seeing a lot of things now, about religion and the way of life that you had become so accustomed to in a different light, having renounced the religion of Islam. I would say that one of the things that can help is to really appreciate this new perspective of yours. Sharing these insights on the forum can be an excellent form of that.
It can also help to contain the urge to rebel, or act out in some way, against the things that you see around you that you know are wrong. At this point I take it that you are still young, and maybe dependent on your family in some ways? The reality is that looking out for one's safety needs to be the first priority, and this requires being careful, both in public and in front of family. I hope you have also read about how to access the forum from a muslim country: http://www.councilofexmuslims.com/index.php?topic=8070.0
Anyway, I hope that you do not take any rash choice. You are right in that eventually your parents would come around if they love you unconditionally, mine are able to be supportive of me as if I had never left Islam. However, you should probably wait to tell them until your situation is more secure. I wish you the best of luck, and hope you are not daunted by the situation. Gaining perspective outside of Islamic dogma is a very rewarding experience, if you can have patience for its challenges. And please feel free to seek out more, and specific advice, and you can always pm me as well. Cheers!