Ben,
Great first project. Congratulations. There's a couple of reasons I would get the Domino (I do not own the WoodRat but have thought about it some. I did have the Leigh FMT jig, which was wonderful, but it sold to make the cost of the Domino a little easier.) 1. As Jerry says, you'll use it on every project. When a M&T is faster than almost any other joinery method, there's no reason not to use them extensively. 2. Speed. I know there are a lot of hobbyists (who dont own a Domino) who think that time is not important for them because they are not professionals. For me, the time is just as important as it is to a professional, but for different reasons. When I saw in the Wood mag video that someone posted on here that it took just 45 mins to mortise and assemble a rocking chair after milling was completed (compared to 8 hours the old way), I realized again what an exceptional machine the Domi really is.
I have to fight for every minute I get in the shop, and would rather build two tables or cabinets or whatever in the time I have available than one.
My $.02. Good luck with your decision and congratulations on geting rolling with a bang in woodworking.
Dave