I'm 100% sure OP will be fine.
There's no way in hell that a single GTX 570 would over-tax a quality 1000W power supply.
How do I know? I have a heavily overclocked and over-volted GTX 570 in a heavily overclocked and over-volted system ... with a 560W power supply. Yes, it's quite possibly the world's best 560W power supply and has a single +12v rail, but still...
All you need to do is make sure the 6-pin power connection and the 8-pin power connection come from different +12v rails. "How?" you ask...
1. Use either the fixed 6-pin or the fixed 8-pin. DO NOT use both fixed PCIe power connectors.
2. Use the other from a modular cable.
Examples: If you used the fixed 8-pin, use a modular 6-pin. If you used the fixed 6-pin, use a modular 8-pin.
The fixed 6-pin and 8-pin connectors use +12v rail #4, and the modular 6-pin and 8-pin connectors use either +12v rail #2 or #3.
Edit: Or, your graphics card might have two 6-pin PCIe connections. (My GTX 570 uses one 6-pin and one 8-pin, so I forget that some use two 6-pin instead) If that's the case, use one fixed 6-pin power connection and one modular 6-pin power connection.