You've pretty much already crossed that hurdle.
You have proven you're able to get along with her. You've expressed an interest in heirs and marriage, and it is a fortunate arrangement for her. You are a well-mannered knight, with a reputation for courage, and have faced evil and won.
Now the ball is in his court, to see if the dowry is enough to entice you. He lives on a stipend from the Earl, so he's not going to have a lot of cash to sweeten the pot, but if that's not an issue for you, he's unlikely to complain.