I need to catch an early morning flight from phuket at around 6.00am. Is it easy enough to get a taxi from the beaches to get me there at about 4.00am? Taxi would have to leave karon about 3.00am I suppose. Are there any cheaper alternatives?

Personally I only ever get to the airport an hour in advance and at that time of day there is no traffic. So I would get a taxi at about 4am earliest of which there will probably be quite a few or just ask someone the night before to pick you up (they will rarely turn down the chance to make 600 baht)

No cheaper alternatives unless you know someone with a car...bear in mind its 40km one way

stay in a hotel close to the airport the night before, maybe 500 baht and a good night sleep!