Hi there!
Firstly, many congratulations!
Secondly, I'm a twin mum myself, so I would recommend you find your local twin club, and give them a ring. Twins and multiples are a completely different kettle of fish, and there are some things that only a twin mum will get!

Thirdly, should you go to Disney or not? Well, fom my experience, I would say no. (sorry!) In the first place you would need insurance, which as soon as you mention 'twins' becomes mega bucks. Then there's your health:-
1) Sickness. You say you are over it, which is great it that's true, but mine lasted 8+ months, and also suffered with chronic heartburn

Yuk!
2) Comfort. Mums expecting twins usually expand, quickly. You can expect to gain an average extra 3 stone, maybe more. Put that together with a 9 hr flight, uncomfortable seating, constant visits to the loo, babies kicking,, swollen ankles, increased risk of DVT, get the picture?
3) Weather. Carrying twins is tiring. So you've done the flight, and feel shattered. Then you have to deal with the weather. I haven't been in Aug (1st time this year!), but I'm expecting it to be HOT!! I was pregnant through a particularly hot May/June, and believe me it's no fun, feeling hot and bothered and carrying so much extra weight; plus you have to take into account the risk of increased blood pressure etc
4)
DDP. Do you really want your first experience of the DDP to be hampered by a twin pregnancy? Strange cravings, not being able to eat and drink all you want.
I know I sound like a real party pooper, but if you feel ill while you are there, it will be ten times worse than if you were at home.
I also know how looking forward to your anniversary trip you are. One of my twins and I read your wedding trip report. We loved it, and your photos were wonderful!
Just weigh up the pro's and con's. I know you said the docs have ok'd the flight, but what about the rest of the holiday/heat?
Just make the right decision for you and your family!!
Jules x