There is a way to change her status here in the U.S., as long as she can demonstrate that she has been maintaining valid F-1 status with the OPT (i.e.: working for an employer in her field of study) and demonstrate your marriage (just the marriage certificate is fine here).
She need not be of the same nationality, and the process takes roughly three to five months - it need only be filed before her F-1 OPT expires, need not be approved before this.
Alternatively, she CAN go back to her home country and apply at the consulate for a visa stamp, and will need to do sop when she next travels in any event.
Speak with a lawyer to clarify the process, costs, etc.
As a dependant spouse, nationality is of no issue. You should file within 6 months BEFORE her status expires in the United States. Filing a change of status from F-1 to E-2 dependant spouse is possible in the United States without leaving. You must be married before she can get a derivative benefit however.
The wonderful thing about an E-2 dependant spouse is that once she receives her E-2 she can then apply for separate work authorization to work anywhere she wants!