As a Manchester Native who now lives this side of the pond, here are a few things I would be aware of:
1. Jet-lag and time difference
While people attempt to get on a 'sleeping' pattern to get over any element of time differentials, the big thing isn't sleep, it is eating. Your body is accustomed to eating at particular times (think 'Pavlov's dogs'), and so the quicker you can get your body eating at times that replicate Florida time the easier it will be to get cracking.
2. Weather
I know people 'know' it is hot and humid in Florida, but this isn't like Spain, Majorca, Ibiza nor Tenerife. The heat is excessive and the humidity is ridiculous. If you are not well prepared it can be extremely overwhelming and debilitating, especially when coming from moderate climes. Without kids makes it a million times easier, but just be prepared to be uncomfortable and know when enough is enough. September tends to be one of the hottest and most humid periods, the weather will be hot and there will be lots of thunder storms given the humidity and weather systems in and around the south east. The closest i can compare is like being out in the mid-day sun in Tenerife / Malta, and being in a Sauna at the same time lol...
3. Parks
September is a great time to go to the parks, the local schools are in session, schools around the country are in session so there will be a big drop in attendance. This is usually why 'we' go at this time if we can, the down side is that there tends to be more closures for repairs, upgrades etc.. as it is not peek time. That said, there will be a big upsurge in foreign visitors... such as yourself of course, but just be mindful that the parks will still be relatively busy and with a lot of people in there who do not necessarily have the same opinion and value on 'personal space' nor 'manners.
4. Enjoy all amenities
As you will be without kids you can spend time visiting the various amenities the hotels and parks have to offer and not have to deal with kids pulling at your hand and wanting to go on 'Its a small world' for the 100th time! lol. Enjoy the hotel and pool, visit different hotels and check out what they have, Disney World is much more than theme parks but many don't ever find that out as they focus solely on the parks due to the notion they are there with kids!
5. Get some comfortable 'trainers'....
we average 30-40miles per week when there pushing strollers in the park with 3 kids, you will be doing lots of walking so pick a pair of 'trainers' that you will be comfortable in. And on that note, i simply take a lot of cotton t-shirts and nike dryfit shorts and change often!
6. Enjoy it!
Disneyworld is the holder of dreams, but i can hazard a guess it is also the graveyard of many relationships! lol... sad but true!