I think with that budget you should be fine to get somewhere really nice. When travel agents hear honeymoon they immediately think Carribean which is very very expensive and you will struggle with your budget.
You will get alot for your money other places such as Thailand, Malaysia and India for example - and some of the accomodation is amazing plus eating out locally is cheap as chips, its also a fantastic experience - great beaches, stunning wildlife and great food. You could always combine it with a city such as stopping off in Hong Kong/Bangkok etc then going onto a beach destination for some R&R. Jan will be hot!
Also Mexico does good all inclusive deals - i'm going there in March and for 2weeks all inclusive 5* hotel its about £1,600 so slightly over your budget but different hotels will be cheaper.
Good luck!