It was only when Alicia reached the level of 10 Friendship and 10 Love that her final Courtship Request appeared on the Bulletin Board. I had her at 10 Friendship Heartslong before I had her at 10 Love Hearts. Even so, the Monster Contest raised the remaining Eligible Girls, including Alicia to 10 Hearts.
She must be at maximum heart level before the Request will appear because it ends in an actual Marriage Proposal. If you do not wish to propose marriage at this point, however, you will be able to take the Special Proposal Item with you for possible future use. It is a Crystal Ball.