Definitely go for a week! It's only 9 or 10 hours on a direct charter flight. If you're clever, you may be able to get an extra day or two by flying with a scheduled airline via Bombay, particularly if you choose to leave on a Friday evening and fly back on a Sunday morning. We did that at Easter for just over a week - picked out a flight that left Heathrow at 9pm-ish so went directly to the airport after finishing work. We flew out of Goa at the crack of dawn on Sunday morning, waited for a few hours for international flight back to Heathrow and the time difference meant that we were back in Heathrow by about 6 pm in the evening. Back at work the following morning, the jet lag works in your favour as it wakes you up and nice and early for the first few days back at work.
Although I'm going for 4 weeks at Xmas, I'm looking out for a cheapie on 28 November for one week charter flight as I've got a bit of additional leave to use up. If I see the flight cheap enough, I'll head out just for a week, notwithstanding that I'm going out a fortnight after my return in any event!!
I have managed in the space of a week to have 3 days in Hong Kong followed by 3 days in Dubai, 2 overnight and 1 daytime flights - Goa for a week is easy!
Carpe Diem!!