I assume you're close enough to the port that getting there is not that big of a deal? I'd see if you can get a rapid PCR test anywhere near you to at least have a better idea of the likelihood of being turned away, but considering you'd get a refund if you were, I don't even know if that matters. It's not like you'd have been planning it for such a long time that getting turned away for a negative test would be devastating or anything.
Those who've booked and dealt with the Safe Passage system for verifying your vaccination status, etc., would be better equipped to tell you whether that's something that needs more time. I'm assuming if Disney is allowing it to be booked, that's not an issue though.
I wish we lived close enough to book last minute cruises (we'd have to already happen to have the time off from work though too).
Maybe because I'm just jealous of the freedom and ability to do it, but I imagine a last minute trip like that could turn out to be a really great trip.