Venice with a 7am departure flight?

Yes if you want to take a water faxi to the airport. Otherwise I would stay within walking distance of Piazzale Roma. Buses to the airport start from there at 4:20 am.

If you are near San Marco and take the #2 Vaporetto, the earliest you can get to Piazzale Roma is 5:33 am, then you wait and take the next bus.

http://actv.avmspa.it/sites/default/files/Orario_linea_2_dal_2_nov_2016.pdf

I did not check the Alilaguna schedule to see what time it starts. It might work too--- takes about an hour to get to the airport so allow for that.

Private water taxis run 24/7 ; your hotel can arrange for one to pick you up on time for your flight.
It is not cheap but your flight time I would be worried about anything else and this method will allow you to get as much sleep as possible.

The "N" boat runs all night between Piazza San Marco and Piazzale Roma.

We took a water taxi in June to Marco Polo . Fun and lovely way to go but it is a long walk from where the water taxi lets you off to the terminals.-about 15 minutes because you have luggage to haul. This may be changing as there was a lot of work being done in the area but the easiest way would be to take a taxi or bus from Piazzelle Roma which will leave you off directly by the terminal. I don't think the airport is even open until 5:00AM. Linda

Linda's point of the long walk from where you get dropped off by Private Water Taxi to the airport terminal is valid.
It is a good 10-15 minute walk. All on flat paved surface/walking path and the way to go is obvious so not difficult with rolled bags but longer than I had expected especially since this is the luxury way to do it.

All factors considered though, I am sure this is still the fastest way though and at such an early hour what I would recommend.