Yeah you'll definitely need a new radio/head unit. Doesn't have to be double DIN, that's just the size. There are single DIN units (half the height) that should have the subwoofer outputs you'll need.
Do you need the door panels with the shaker system? Not necessarily, you can also get a subwoofer box that goes in the trunk.
But the main thing is you'll need a new radio with subwoofer outputs on it. And the other catch is you'll need an amplifier to drive the subs too. There's two kinds of audio outputs, line-level and speaker-level. Line level are you're pre-outs, they're like hooking in your DVD player to your TV. They're low voltage (2-5V) and aren't strong enough to move the speakers at a volume you can actually hear. They're just there to send the audio signal to something that can.
Then there's the speaker-level outputs, which are a higher voltage and stronger signals that actually can move the speakers at listening volume.
Most radios have a small built-in amp that gives you the speaker-level outputs to drive the 4 main speakers (you'll see this in specs as 4 channels, usually ~ 15W RMS/50W peak power) but I've never seen one that has a built in amp to provide speaker-level outputs for the subwoofers. All I've ever seen is having the pre-outs/line level outputs for the subs, meaning you'd need an external amp to amplify them up to speaker level. Even the factory Shaker 500 has separate amps for the subwoofers (on the left wall above the driver's side footwell).
So you might be looking at one of the following options:
- new head unit
- Shaker 500/Shaker 1000 door panels with subs
- small 2 channel amplifier for the subs (you have to be careful about the power level of the amp -- too strong and you can burn out the subs)
Or a more OEM-like setup (if your car already has all the wiring under the dash for the Shaker system)
- new head unit
- Shaker door panels w/ subs
- OEM subwoofer amplifiers
Or go completely aftermarket
- new head unit
- shaker door panels, no speakers
- new 6x8 speakers for the upper doors and rear deck
- shallow mount 8" subs to go in the doors (Kicker used to make a compatible set)
- 6 channel amp (4 channels for the main speakers, 2 for the subwoofers)
Hopefully this helps get you started. Ther're a few threads on the forum about different pieces of this. Also check out Crutchfield, they've got a great site and great advisors too.