oceanmarina,
Part of the answer lies in knowing when you are going on the cruise.
But first let me say that if you want a table by your self, I think you do have a better chance at second seating than first seating as first seating seems to be the more popular (at least I've never heard of someone being wait-listed for second seating). After all, this is the Disney boat, so there will be lots of families with children, and the general rule seems to be that parents don't want to be feeding their kids dinner at 8:00 at night.
The reason I say the answer depends upon when you cruise because on our recent cruise in late October, I heard it said that the boat was only at about 80% occupacy. Our family of three got a table to our selves, and all we asked for once we boarded was to be changed to 1st seating. And at that first seating, there were several empty tables and therefore someone such as your self would not have had a problem getting a table alone.
Regardless of what you might request or get before hand, all you have to do once on board is follow the directions in your navigator for requesting dinning changes. That's when they (
DCL) really have all the information about how many are dining when and you very well might be able to get your request fulfulled once on board. As an example, we had asked for and got wait-listed for first seating for this recent cruise. Despite the fact that the ship was only 80% full, our request was not honored before we boarded (I assume it has something to do with keeping early and late seating balanced regardless of how full the ship is). But like I already said, once on board, it was a non-issue getting it changed to what we wanted.
BTW, I know that fall season (after the kids are in school and before the holidays) is at least one of the slower seasons for DCL. I'm sure your request is more likely to be filled if you go during an off season. Not sure what else are the off-season times to go.