If my girlfriend has been diagnosed with genital HSV 1 and I have oral HSV 1 how likly is it that I can contract HSV 1 genitally as well?

Won't happen. You already have immunity against hsv-1. If she had hsv-2 you could get it but since you have antibodies to that virus, hsv-1, it shouldn't be an issue.
Less likely. It is possible that your girlfriend's genital outbreak was transmitted from your oral hsv1. Men are lessnlikelybtonhave genital outbreaks because the virus likes moist mucosal surfaces better and men don't have that as part of their genital anatomy like women do.