Of course you can file now and see her in a few months; however it may not give you the best chance of approval.
It seems like you are really excited about this whole thing!
From all of the messages on here, it also seems you may be recognizing red flags in your ability to prove the validity of your relationship. Many of the responses here seem to be suggesting you may want to take more time getting to know one another both to help settle your concerns as well as to help settle the concerns of a visa officer. As I read it, while you seem to share similar cultures, some of the major concerns from an outsider's view might be:
You have not spent much time together
You have not known each other very long
You seem to be in a rush to get her over here
The online engagement ceremony and engagement certificate may actually confuse the issue
While most of us are anxious to get through this process and be with our love one, the primary cause for visa denial is the perception that the relationship is not genuine. Additionally, a fiancé visa will not be issued to a married couple, and there is no formal engagement process in the United States. There are numerous examples of denials based on appearance of marriage (dowry payments, formal engagement parties, photos that appear to show a wedding ceremony, etc.).
Obviously every culture has different approaches to these things (e.g., a dowry/bride price in some cultures may be required before the family allows their daughter to move, and in other cultures it actually signifies that the couple if officially married), so each case is different. Even so, it would probably be advised by most people on here that you simply follow the steps outlined in the guides on here and any country-specific advice you can find as well. People have been through the process and some of the respondents have seen so many things as they have been contributing to this site for well over a decade.
Hopefully you can get this all sorted out and move forward with whichever option you feel is best for your situation and the two of you can be reunited soon!