I am also on this cruise with my husband and 2 little girlsl, and they are now sooooo excited as they have never cruised before. See you there.
It's normal these days for the ship to cleared by 9.00 - 9.30am. Remember they have to reload the next lot & that usually starts at 11.00 - 11.30 am. As ships get bigger they need to clear them ASAP as loading takes considerably longer & don't forget you have the option of getting off earlier if you so wish.
There are normally loads of taxis waiting but I must admit that sometimes you have to queue so if you can arrange a private transfer, although normally dearer, it is better. As Bill says 9-00 and you can normally arrange with reception to have your disembarkation for say 8-45, or for that matter just go ashore then as there is often no real check. You might also consider a rental car for the period of your stay which could be picked up at the docks and dropped off at the airport and makes you far more mobile especially if, as I assume, your flight isn't until the late afternoon and probably evening of the next day. If you have never driven in the US it is not difficult and let’s face it, if you can handle the Swindon Magic Roundabout you can drive anywhere. Regards ... Neil.