Can't add any more to the advice to help keep costs down, but can add that I would say a definite "
yes" to "is it worth it for a week?"
Most of our trips have been for two weeks, but DH, DDs and I went for a week's trip over NY once, stayed onsite and went into commando mode to see/do all the Christmas / New Year attractions and had a great time.
I went with just my mum for a week and we managed to visit all WDW parks plus SeaWorld and Kennedy Space Station, and still took it all at a fairly even pace - it did take some planning, though
In the middle of March DH and I are off on our first trip without DDs - for
6 nights

We're going because I got a great deal on Airmiles, and chose to go for 6 nights rather than 7 because of work / family commitments. We won't be visiting any of the parks, however. (I can't wait

)
I suppose I'm trying to say that a week is certainly 'do-able' and definitely enjoyable as long as you know what you hope to achieve and accept that it can't be the same as a two-week trip.