Dudette, I'm probably not going to be much help, but as a female Aspie living with an NT boyfriend, here are my views. Of course, bear in mind that your girlfriend might have totally different expectations.
I wouldn't give up right away, because if you 2 have already begun seeing each other more seriously, she might be more hurt to end things than your typical girl, because of rejection. As others have said, we're wired differently, so this implies that there are things about us that are completely different to what you would expect, and the fact is, we can't do anything about it. It's not a lack of will, a lack of love or a lack of effort, it's just how we're built. Think of it as dogs and birds: both are animals. They may live in the same place. But no matter how hard you try to teach your dog to fly, he won't, because he's not built for that/like that. Likewise, aside from very specific species, you won't be able to teach the bird to bark. And it's OK. So that's something you need to accept as a fact if you hope to build a relationship with her.
Most of us have tried the best we could to fit in. Some manage to wear that mask and play that role so well that they definitely look the part, and others try, but are less gifted with mimicking NT behavior. Either way, it's exhausting. Physically, emotionally and morally draining. Please keep that in mind as well, it also means that sometimes your girlfriend will need a safe space where she can retreat and recharge before interacting again.
Also, don't be worried if you feel you have fewer interactions, that doesn't mean they can't be quality time. But they will be different.
Like Judge said, you will feel like you're pulling more than your weight in the relationship. I might add that you might feel like you're the only one making efforts, and she's being selfish, and so on. Try to find a way to communicate on difficulties the two of you may encounter. Personally, I argue with my boyfriend over text messages, each of us in one end of the apartment. I get to say what's on my heart in a non-intimidating way, he gets too avoid seeing my meltdowns, which he still can't handle too well, and I feel that this saves us a lot of stress during arguments (which I'd much rather avoid, but some people can't communicate otherwise).
What else may I add? I think if you do want to carry on together, it would also help a great deal if you researched how Asperger's work, and also how it works in women, since there are a few twists. Familiarize yourself with the concepts of sensory overload, find out what things are unbearable for her, and what things make her feel better. On that note, you might want to ask her view on hugs. A quick search on the forum will show you that we are very opinionated on that topic.
You'll never understand it from first-hand experience, but that doesn't mean you can't understand how to be in a relationship with an Aspie. You just need to be aware of the differences and be open-minded when said differences seem overwhelming.
Anyways, this is long enough already. You have met someone who will probably be the most unique person you'll ever meet, which comes with good sides and not-so-good sides. Seeing you ask a question here gives me hope that you care about her enough to try and do well. Good luck!