Would it be worth to take a Taxi from Hangzhou to Qiandao Lake?

Well, first of all, one taxi can only accept at most 4 passengers. So it's better to hire a private mini van for you. In general, the fare is CNY 800 to 900 for the round-trip.
It sounds like a little bit expensive. If you wanna choose public transportation, take direct coach from West Bus Station. The schedules are from 06:30 to 18:50. It costs CNY 60 to 70 per person for single trip.
You can choose the way you like.