A breadboard is a bare circuit board with holes in it to set your components and conductors. You can find them pretty cheap at Radio Shack... normally they're brown or green fiberglass (I think) boards with a bunch of little holes in them. They should be labeled accordingly.
Another option for the vibrating motor is a pager. I could mention a few other things that you could get the motor out of, but I probably wouldn't be throwing too many ideas around after that. Anything that once vibrated will have a vibrating motor. As far as stronger ones go, you're gonna need to look into the afore mentioned unspeakables. Best I got on that... can't really think of any vibrating motors that are stronger than the ones they put in those things.
As far as gearbox goes, they're a brand of external hard drive. At least, the gearbox is the only brand that I've seen with a clear plastic cover on them. Gearboxes come in many different variations and can be found at most PC stores. Take the HD out, strip the internals, and you've got a box about the size of a HD to cover anything you need. They're normally plastic, but I've seen them made of aluminum and even diamond-plate. Most all the materials they're made of can be drilled, so a switch or LED hole would be easy to make.
Covering the device is definitely a good idea. I wouldn't be too afraid of him being shocked by a DC source, but he may figure out that those LED's come off if he tugs on them enough, and decide to eat one... and I can't say that LEDs are edible.
If you decide not to go with the gearbox for the cover, there are many other options. You could actually build a multi-level plywood box so that he would have to look through a slot to see all the flashing lights and stuff. That'd make it better because he'd be safe, and the LED's would have a shade over them to make their effects even more extraordinary to a 6 year old.
I think, though, that if we give you too many more ideas, the kid will be 20 before you even get the thing built. I think you've got the basics, and you know what you need for what you want it to do. Give it a shot, and post pictures.
-Will