First and foremost, don't marry people you work with. It is a relationship most people do not know how to have. Your work life becomes your home life, and you have no home life because it is your work life.
I think she is probably very intimidated by such quick actions, I agree with you there. These feelings may be why she said she has no internet. I know I have fibbed like that to people when I want them to stop bothering me about something.
She may have different approaches to this "relationship" and I highly suggest that you spend more time with her before you send any impersonal messages online about wanting to marry her- this will not sit well for most women.