It's done and it went very well.
Like I said I would, I just blurted it out without any preface. She wasn't ready for that as she thought I planned to move out of my father's place and needed her help. I explained to her why I wanted to tell her and she took it really well. Then, she asked me the traditional questions which I was ready to answer. After that, we talked about the road ahead and everything I need to do.
When I mentioned to her, somewhere in the conversation, that unless I needed to go out I was always dressed she asked me if wanted to do it now. I told her yes and she told me to go change. I just put on a simple dress, cotton tights and flats, and returned. When she saw me, she complimented me, asked me if I felt better (yes), hugged me and we resumed talking like nothing happened.
Before she left, she told me that she will research it on her side to understand it more and will come back to me. I asked her her email address, in case I didn't have it, and told her I would send her some documentation to help. We hugged, then said goodbye.
Now, I feel better but I'm still a little stressed because there's still a lot of people I need to come out to. One of them is my mother.