Take a taxi to the Dubai Mall. It’s about 20 minutes from the airport I believe. You’ll be in the middle if 3 of the top attractions: The mall, Burj Khalifa & Dubai Fountain. There are lots of shops and cafes around. It will be a pleasant way to burn up a few hours.
This is a good idea in theory. The problem with Dubai Mall (or any Mall in Dubai for that matter) is, that it can get very difficult to get a taxi back to the airport from there close to midnight, as most shops close at that time. I had a stopover of a few hours in Dubai last year and went to Deira City Center to do some shopping. The advantage of doing that is, that instead of queuing for a taxi you can take the Metro from the airport to the Mall. It’s just two stops.
However on my way back to the airport I still needed a taxi, firstly because I did a lot of shopping and secondly because the last metro from Deira City Center leaves around 11.30 PM. I was standing in a queue for more than an hour until I finally got a taxi. Luckily I still had a lot of time left until my flight was to take off so it was not a big issue.
So if you want to do that, make sure you account for enough time to get back to the airport in time. You’ll land at 7.45 PM so that means you’re next flight will be around 2.45 AM. That would mean the following schedule:
7.45 PM: Landing in Dubai
ca. 8.30 PM: Getting out of the Airport and in a taxi
ca. 9 PM: Arriving at Dubai Mall
ca. 11.30 PM: Reach the Taxi Waiting area at Dubai Mall and queue for a taxi
ca. 12.30 AM: Take a taxi to the airport
ca. 1 AM: Arrive at the airport
As you can see this gives you approx. 2 1/2 hours to spend at Dubai Mall.
The working week in Dubai is Sunday to Thursday. Since you are arriving on Sunday evening, most of the shops in the malls will close at 10 PM. The supermarkets (Carrefour, etc.) and the foodcourts will remain open until midnight though, as mentioned above.
Catch a movie at Mirdif City Center (closest to the airport). I really don't think it's worth the hassle of leaving the airport as most things are closed... except if you want to go on a drive to Marina, Atlantis etc.