The Vaporetto runs all night during the peak season with boats leaving approximately every 30 minutes. You can get to Piazzale Roma early in the morning. From Piazzale Roma, you would need to take a taxi to the airport. It is doable, but given that you should be checking in two hours before your flight, you will be up very, very early. If you want to be at the airport by 4:45 am you will need at least an hour for the Vaporetto and taxi.
I would at least consider staying near the airport. It would eliminate many of the things that can go wrong such as missing the Vaporetto or having trouble getting a taxi at Piazzale Roma. You’ll still be getting up very early, but you will have reduced many of the problems that come with using public transportation at such an early hour.