"Low light and quick shutter' is exclusively a capacity of lens, not the camera. The ISO may seem like the big difference here, but an f/1.8 maximum aperture will do a lot more for low light/quick shutter than ISO 3200 over 800/1600 does. In any event, a kit lens included under $1000 is far from ideal for this specific puirpose, the cheapest option at your disposal for this purpose is the 50mm f/1.8 at ~$110. Its available on every camera mount. Look for anything in the range of f/1.4 to f/2, as fast of lens as they get. (well, the f/1.2 and faster are ridiculously pricey)
The Sony NEX is a series I am extremely excited for, however - for the purpose of 'low light quick shutter', you will have a much wider lens selection available on standard DSLRs. For the time being, the availability of fast lens on these compact EVIL cameras is scarce (Olympus/Sony). If I'm up to date, then f/2.8 is the fastest lens available for any small EVIL camera. The Sony NEX series DOES have an AF Alpha mount adapter, which opens up the selection a ton, but you'll lose AF ability, and once you add a full size lens plus adapter, you really aren't that much smaller than a DSLR anyway.