I have seen the nighttime parade at Disneyland and you should have no difficulty taking pictures of that.

The lighting is so bright, that just about any digital camera should do a good job.

Just remember, while taking pictures of the parade, make sure that you have the flash turned OFF.
The flash is too weak to be useful and having the flash active will force the camera to use a shutter speed of 1/60th of a second.
Just hold the camera steady and lean against a post if possible.

Most digital cameras have a shooting mode for fireworks, use it.

Just remember, for good fireworks shots the camera will use a slow shutter speed. find a place where you can set the camera on a fence, post, trash can, or whatever. You need something to help you hold the camera steady for at least a second or two.

You didn't say how much you expect to spend for a camera.
They range from $100 to $550.

If you need something soon and in a hurry, pick up the Canon A1000.
It sells for about $150/$160.
Buy some rechargeable NiMH batteries/with charger. About $15-$20