She can marry you. However, you should look to see is she is subject to the 2 year foreign residency requirement. If so, then regardless of your status, she would have to leave or obtain a a Waiver.
Brian D. Lerner
Attorney at Law
She can marry you during her J-1 stay or before entering the US. If she is married to you, there are challenges in her seeking a change to F-1 status because she may find it more difficult to prove that she has sufficient ties to her home country showing that she intends to return upon completion of her studies. Depending on your and her long-term plans, it may be better for her to change status to H-4, which would allow her to study full-time in that status. Of course, the drawback would be that she would not be able to work at all during her studies, nor get OPT following graduation. All this assumes that she will not have a two-year return requirement through her J-1 status.