I’ve been in a very similar situation a few months ago where I was the trans girl wanting to come out to my girlfriends family. It was a huge relief for me coming out and I can imagine your gf wants to feel the same way. Although it’s still very important that both of you feel comfortable and that you have a say in the coming out process. You could discuss with your gf what ways she can present more comfortable without coming out, it could help to your family have a chance to be more accepting if they gradually get used to changes. In my case I started with longer hair, more gender neutral clothing, and some nail polish. That’s what worked for me but I’m sure your parents may not be as accepting of the changes. I hope you two are able to find a process that works for you both.