Unfortunately, you both have to be married on or before the date your gf had been approved for asylum for you to be eligible to apply for your derivate asylum status and green card later. If you guys are not yet married, you aren't eligible to apply for GC after a year, based on your gf's asylum approval. Only she can apply for her GC after a year even though you guys get married now.

Are you both in the US? What is your status? If you are on F-1, then you guys can get married now. When she gets her permanent resident status, she can file for your GC. But still, you need to wait 2-3 years until your priority date becomes current to apply for Adjustment of Status. 

Correct me if I am wrong.