It could well do the trip, but...
If you are prepared to spend $1000 on a new bike, I'd say call around dealers, to see what there is second hand for that price.
I'd say that an older bike from one of the Japanese companies (regardless which style you choose) would probably be a safer bet in terms of reliability than a new Chinese re-hash built with probably less quality control than my Ural!!
Models like the CB or CM250, a late GN250, even bigger Dual Sport bikes: DR 350 perhaps... even a C90!!
Plus a chinese bike would be worth next to nothing at the end of the trip, where as one of the bikes mentioned above could well fetch a healthy share of what you shelled out to buy it...
Adventure: it's an experience, not a style!
(so ride what you like, but ride it somewhere new!)