I had one of these autos in my Supra and it was fantastic fun off the line. I converted it to manual, but now that I'm building a project car I'm using the 1JZ with the same auto box behind it.
You shouldn't experience any problems at this kind of power level. To my knowledge these are fundamentally the same A-series automatic gearbox Toyota has been making for 30 years and used across the majority of their model range (RWD ones, at least).
To support these kind of power levels I reliably would suggest that you should do the following:
* clean the filter (believe these are a metal one you wash rather than a consumable item)
* flush entire box & torque converter with new fluid
* have the valve body modified for firmer shifts (MV Autos in Adelaide do it for ~$400 exchange, unsure if you have anyone local)
* fit an upgraded fluid cooler
Many people would recommend a larger stall, however I assume with these power levels you will be retaining the standard turbos. In this situation it should get off the line quickly with a minimum of fuss!
If you go for a bigger turbo later, you can have the stall modified and the box itself built (again, MV can provide this service).