^^^ My car idles @ 800-850rpm - so I don't think at 1000rpm that it's too low.

Shaking on idle would mostly likely be your mounts, either being split open or loose.. Get it under a hoist and inspect all the mounts from the underside, saves you alot of time and you will know if they are worn out etc.. For engine mounts, if you see wet marks etc, they're busted. Look out for cracks etc.

I'd say it's drivetrain related. But don't count on it, i'm just giving you my e-opinion. lol Get it checked out by a reputable mech if all else fails.