Will be arriving in Prague at 1130, and leaving at 0700 in the morning. What is the best way to get from the airport to the Grand Hotel, especially to make the 0700 flight?

Didn't mean this to sound like I was leaving the next morning - staying a couple of days.

I'm not entirely sure where the Grand Hotel is, but a private car hire through your hotel would be your best bet. I am thinking that is the Grand Bohemia? Maybe not, but I think it is very common for at least 4* hotels in Prague to have an arrangement with a private driver which will be more reliable than a taxi, and reasonable in cost, for a flat rate. I wouldn't even consider anything else myself, but perhaps some others on here will give alternatives.

You can also try a transfer service. I'm using http://www.athos.cz/ which was
recommended on this forum. Happy travels!

I second Christina's advice, have your hotel arrange a taxi or car service. They have a stake in the arrangements going off without a hitch.

Marking for future reference

When I was in Prague, I used a flat-rate van service with Cedaz to get from the airport into the Old Town. I don't remember the exact cost, but I think it was the equivalent of around US$25. Going back to the airport, I asked my hotel to book a regular metered taxi, and the fare was quite a bit less; the driver was right on time. You do need to arrive fairly early for a flight, depending on the airline. For example, the budget airlines had huge lines, while at Czech Airlines check-in took me about 10 minutes.

How long does it take to get from the centre of town to the airport?

it should take between 15 and 30 minutes, depending on where you are. I was able to comfortably catch a 6am flight by leaving at 4:45 from my hotel downtown Prague.