Single mom been cruising with DD since she was 4, on
DCL since age 7. She just turned 13, and wanted a trip on the Magic for 13th birthday.
I actually like my "alone" time. ON some of the trips, she's been very happy in the kid programs, other times, she wants to hang with me. They key is whether or not she makes a buddy in the club/lab in the first day or 2. Go to the "cruise meets" section and see if you can find another family with a same age/sex child. Then do some e-mail correspondence between the kids prior to sailing. WHen they get on board, it is like meeting an old friend.
I like the adult programming on the Eastern especially...I love the rainforest, and for the first time, I tried some of the adults only things (like Serenity Bay while she did the teen excursion). No, I'm not lonely...not ever!
There are activities for "singles, single parents, or travelling alone" which I have done on occasion. Sometimes we sit alone together at dinner, other times we have met wonderful table mates. I don't specify before boarding, but let DCL assign us where they will in that regard. We do request our favorite server.
We read the kid's navigator each morning and decide which activities she wants to do. We generally go to the shows together. My experience is that an 8 year old will do the lab for a couple of 1 1/2 to 2 hour stretches per day...so that's a total of about 4 hours....the rest of the time, mine wants to be with mom. This recent trip was different because she was now officially a "teen" so could hang in the Stack. She spent more time there than she ever did in the Lab.
On day one, go to see the rainforest. If you like it, you can do the fitness room and rainforest every day and enjoy your time alone. Ditto the hot tub and adult pool.