It is very important to know if she has HSV 1 or HSV 2. She can get an IgG antibody test that will tell her. If she has HSV 1, then since you have it already, there is no need to worry about transmission between the two of you. If she has HSV 2, then it would be my advice that she go on daily antiviral therapy to reduce the risk of infecting you by almost 50%. Even if she doesn’t have frequent recurrences, that does not mean that she will not shed virus when she has no symptoms. There are very very few side effects from these medicines, so I’m not buying that argument. It would not be useful for you to start antiviral therapy yourself, no.
HSV 1 orally affords no protection against getting HSV 2 genitally but if you do acquire HSV 2, you are likely to do so with more limited symptoms or no symptoms, vs. the person who has no HSV 1 infection already