Wonderful that you've come to term with being trans. For your partner, it can seem like sudden and unexpected and if you went forward on your way, they haven't had the chance to do so yet.
There is no right or wrong way to come out : your way will be the right way :)
What's important is to do it when you're ready, when you feel safe to do so, as casually as possible, and on your terms.
Your girlfriend may have fears of her own, about your physical evolution (and if she'll still feel desire/attraction toward you), her sexual orientation (like wonder if she can still identify as lesbian/straight ? etc), the social pressure, and of course, all the preconceived ideas she can have about trans people.
Transgender organizations can help to listen to her, to her fears and all, if you don't think you can do it (because, it's not our job to educate everyone, and sometimes we just can't, they're absolutely no shame in that!).
If you feel like it, then you can try to reassure her by giving her access to information and ressources to help her understand better what you're going through, what it means and what it doesn't mean etc.
The most important thing is for her to understand that coming-out is an act of trust and faith. It doesn't mean you lied to her, but on the contrary, that you feel comfortable and trusting enough to share that with her. It doesn't mean you'll become a stranger, but on the contrary, that you'll be able, finally, to be yourself and thrive :)