Sorry to burst the bubble but at $1250Us per month you won't be sitting listening to the surf and drinking a beer at the end of your day; you'll be too busy swatting mosquitoes and lamenting the loud music of your neighbours. The generally accepted amount to live in decent comfort on the island is $2000US per month and that was 5 or 10 years ago. Yes, you can live on $1250US per month. If you're REALLY lucky you can find a 1 bedroom or studio for $500US a month leaving you with $25US a day each to cover your electric, water, cable, Internet, BEER, transport and food.
You really need to think this through, we see people come down here all the time and they're gone and broken within the year. The number of broken marriages are laughable. Only those that can throw away their old lives and keep themselves out of the bottle (or whatever their poison) survive. Sure the snowbirds paint a pretty picture but they don't live here full time and can leave when they want (doesn't sound like that's in your budget).
Take it as you will, I arrived on the island 10 years ago with a duffle bag and a few grand and I do okay but that was 10 years ago; things have changed a lot since then.