That's probably what I'll do if it comes up. The problem, though, is you could theoretically carry your extradimensional space like a balloon around with you. At 12th level, you could extend it to last all day (heck, under 3.0, you could 3x extend it, and just cast it every other day). Why are spells so abusable if you make them reasonable for the normal uses?
I haven't seen any FAQ's or errata or anything on it, but it'd be pretty lame if your rope trick ended up putting you 40 miles from the ship. So, if you want to cast rope trick on the ship, it'll stay at the same spot relative to the ship.
Your rat isn't as noticeable as the hawk and wolf, so it was ignored, in case your wondering. It might have some squabbles with the ship's cat. Interested in a cat fight?