People, her dad is really good. First of all, as the Duke was investigating candidates for marriage, the heroine's father was also looking for candidates. I don’t think he was thinking about duke like real candidate, but one of the famous bachelors could not be counted. Moreover, the status of the heroine allows her to marry the duke. So the father did not just give to anyone he met right now who asked his daughter's hand. He knew that this was a respected duke, someone rich and a warrior who could protect his daughter. They probably know each pther bcs heroine's father and duke are both lead their families and i'm sure they know each other. They probably met at government meetings and balls. So he knows the Duke's personality more or less. And finally, the heroine's father put forward a condition for her daughter to be happy in a noble marriage (it was times like this). Plus, they won't get married right now, now they will learn about each other during the engagement. And the heroine can just break the engagement f she want. Her father, like the whole family, is very good