oh, I just want to hug you! haha. More power to you for wanting to be responsible with this issue!
Being in your position before, I highly recommend using more than just a condom. It is far too frequent that they sometimes break and when they are the only form of birth control that you are using, the situation can become pretty scary.
From a female's, and recent med student's, perspective, there are many many other forms of birth control that can be more reliable and easier to use than birth control pills. It is actually medically recommended to use at least two forms of bc. I personally used condoms and depo provera injections until my partner and I felt able to deal with the consequences of only using one.
I, of course, do not know your girlfriend's, nor your opinions, concerning the specific types and usages of birth control, but I strongly encourage you to look into your options. Physically and medically speaking, I can not think of a way that your girlfriend, you, and a health care professional could not devise a birth control plan. Obviously, everyone's body is slightly different from the next, but with so many options there IS a match.
Lastly, I know I may be stepping way out of line and I apologize. However, I have always had the opinion that if you have made the decision to be mature enough to have a sexual relationship then you should logically be mature enough to be responsible about your, and your partner's, health and safety. Unfortunately, far far too many people apparently do not agree. I completely congratulate you on wanting to be responsible. There needs to be more people like you out there. Good Luck!