No, if she only has it genitally, she is only infectious from her genitals. She is not infectious from her mouth.
Do you know if you have hsv1? Well over half the population does (your chances go up as you get older), and 90% will never get a cold sore. Ask your doctor for a type specific IgG blood test to know for sure.
If you've ever had a cold sore, then you have hsv1 already, and your antibodies will protect you from getting it again in a new location. There is another thread on this now which you can read for more info - https://www.medhelp.org/posts/Herpes/Transmission-of-HSV-1-/show/3042650
Genital hsv1 rarely sheds (where the virus is active on the skin but has no symptoms) and doesn't recur often. This makes it very unlikely to ever transmit to someone else, even if you don't have it. If you don't have it, I'd just avoid sexual contact with her genitals if she does have symptoms and not worry about it.