First of all: DON"T STRESS! Consider this first day a gift and just enjoy it for what it is.
FYI, I go to DLR all the time by myself, so here are some suggestions:
Unlike the other posters, I'd probably spend the whole time Thursday at
Disneyland. I never seem to spend more than half a day at DCA. (Between FP and Single Rider, I can cover a lot of ground there). And you'll have the opportunity to visit DCA on your other days. (Personally, I'd start Friday in DL, then cross over to DCA late morning.)
FastPasses might be a problem, especially for Space or Indy. Though they probably won't have run out by the time you get there, they might be for much, much later in the day. Grab whichever one you want first; when it's time to get your next one, just see what is still available. Remember: Roger Rabbit is not on the same FP system, so you can be holding that one, too.
Splash Mountain has a SINGLE RIDER line. By all means, use it!
Other than that, I'd probably try to do some of the major non-FP rides (POTC, Mansion, Matterhorn, IASW, Jungle Cruise). Save Nemo until later that night and/or first thing on one of your mornings.
Whenever I have an extra partial day at the Park, I usually throw in a few of the "take it easy" attractions I might otherwise skip: Tiki Room, Mark Twain/Columbia, Innoventions, Main Street Vehicles, Disneyland Railroad, etc.
Watch the Parade. I'd be inclined to catch the afternoon one on Thursday. Then, when the evening Parade is running that night, you can hit Fantasyland and do several of those rides.
Plan on seeing Fireworks (from the Hub) and Fantasmic! (the second, less-crowded showing would be preferable -- if you're not beat.)
Most of all: ENJOY!