The etymology of BBQ is probably the word "barbacoa" (Taíno folk language--Caribbean) loosely meaning "sacred cooking pit".
The Taino people may have used 'barbacoa' in their language however, the roots of that word seem to go from there back to the Yucatan/Mayan language.
To this end...there is an interesting article that shows the root of 'barbacoa' here - (it's in Spanish) http://www.oem.com.mx/elsoldehidalgo/notas/n769057.htm
This article makes a good case that the root of the word 'barbacoa' can be directly attributed to the Mayan 'BAALBAK KAB' = baal "to cover", bak "meat" and kab "land". It says they used red rocks (heated up rocks)...and placed a slate rock on top to heat up meat etc.
BAALBAK KAB - Looks a lot like words such as Kebab which is Urdu (Indo-European based language)