I don't see anything inherently wrong with a woman proposing to a man; it is certainly a significant statement of how she esteems him. Hopefully she does genuinely esteem him and not see him as some sort of meal ticket.
If the man has not proposed, there is probably a reason why, even if the reason is only, "I haven't thought about it yet."
However, the reason may be deeper. He may have legitimate questions about the "quality" of the lady. He may not be "settled" on that one lady. He may have deeper emotional issues that are really better resolved prior to marriage.
I would suggest that it's better for the woman to pray about it (first and foremost!) and to broach the subject gently with the man. The purpose is to explore the subject in a safe environment. At that point, if he shuts down the subject, she does well to walk away. It's more likely that his concerns will be brought to light, whether or not they are "legitimate". If nothing else, they can both be honest about their feelings and concerns. That alone is great preparation for being married.