My girlfriend has had HSV2 for several years and I have had HSV1 for a short time. Is she protected from getting HSV1 from casual kissing even if I am having an outbreak?

No. one type of virus doesn't protect anyone from the other type. But...there is discussion out there as to whether or not having one type can make the infection of a second type less severe. You still need to be careful not to spread HSV-1 to her. Several people here have both 1 & 2.

Interestingly enough, in ongoing trials, HSV-2 vaccines are proving to be most effective in women who test negative to BOTH HSV-1 and HSV-2. If having one form lent any sort of protection against the other, then you might expect the opposite to be true.