Immigration can be time-consuming, although probably not an hour. I don't know the airport well enough to know whether that hour is a busy one, but I would imagine that it's relatively peak. Still, you will have plenty of time.

Alcohol is like elsewhere in the Middle East -- only available in hotels, although in Doha it's even more restrictive than the UAE, in that it's only in a few select hotels. Surprisingly, the best hotels in the city (Ritz-Carlton and Four Seasons) don't really have Arabic restaurants (they tend to have Italian, for example) and others (Sharq Village, InterContinental, La Cigale) only have buffets, which are quite upscale with lots of the local standbys but perhaps are not what you're looking for. (Also, by the way, the R-C and FS could easily be a 45- to 60-minute drive from the airport in each direction those times of days.) Your best bet might be the Sharq, which is actually a Ritz-Carlton property and is very close to the airport, and has what seem like (I have not been there) very nice restaurants.

Or, for a bit more local flavor, I could recommend the Al Shami Home Restaurant on C-Ring Road near the Ramada (also close to La Cigale). It's a mid-scale, authentic Arabic place with simple food. Also not romantic or opulent (and no alcohol), but it is fun, and you could walk over to the Ramada down the block afterward and go to Bubbles on Two, a very nice champagne bar. (I know that you think of when you think Ramada, but this is actually a nice four-star hotel with some excellent food and beverage outlets.) There's also the Pearl nightclub at the Marriott (next door to the Sharq), which is pretty nice.

Hopefully someone else on this forum can recommend an upscale Arabic restaurant in the city (to Reteli and to me). . .