Maybe dad thinks you will do some of the wild things he did during his 27 visits ☺

IMO Judy House and Sue are a great home base. Four years ago when I went for my first long visit (3 months) I was a bit nervous, so I chose her place and it was a good choice for me.
Now that she also provides hostel rooms, there are lots of younger travelers like yourself coming through to stay there. You could ask her if she has bookings yet for that time of year or what she thinks it will be like then, to give you an idea if it will be lonely or people to hang out with. I'm sure she will answer any questions you have.
The suggestion to bring a friend is a good one, although part of me thinks nah, that's just more work and what if she turns out to be a wild one that you have to look out for and worry about?
September is the slowest time of year for tourism, and a financially pressured time for residents with children going back to school. As a solo traveler your vacation might be more fun and relaxing if you go in August or November.
Plan to be back at your home base by dark unless you are at an actual venue (restaurant, bar or concert) and taking a taxi back to Sue's. Dark comes early in the evening. There is plenty going on up at Sue's to keep you entertained at night if you don't have somewhere else to go.

Ask your father what specific concerns he has about you going alone. Then discuss how you might handle those issues for a positive outcome. He probably has some valid things that you should listen to, and you can use his recommendations to plan a good trip for yourself.

PS There is a nice little beach for snorkeling and swimming by Canoe Bar & Grill, at the bottom of lane from Judy House.