Basically, you answered your own question. Why would a 600 watt amp kit be big enough for a 1000 watt amp?
You need a Minimum of 4ga power and ground, and thats just for the mono amp. If you intend to add an amp for your front drivers, you will need bigger.
The safe bet is to go up to a 0ga amp kit.
Another issue I see is that that amp is not rated stable at 1 ohm (according to kickers website it is good to 2 ohm)
Your dual 4 ohm subs can be wired to present a 1 ohm, or a four ohm load at your amp. Since you cant run at 1 ohm, you have to go to 4ohm, which means your subs will be sharing 550 watts. That certainly isn't a bad thing, and should be plenty loud, and your amp will stay cooler pushing only a 4 ohm load.
Do some research about amplifier and subwoofer wiring before you decide to tackle the job, as well as on how to properly set amplifier gains.
I did a re-wire this weekend for a guy who hooked up his RE Audio XXX sub to a 2500 watt amp, and had the DVC's wired wrong. Smoked a $700 sub in less than a minute
