Warped rotors or something else?

Another vote for rotors

I had the same problem with a 2000 Jeep Grand Cherokee. The rotors from Jeep were POS's and warped within a year. The vehicle would shake at mid and high speeds (above 40MPH if I remember right) when the brakes were applied. They dont shake at low speed because not enough energy is stored in the wheel at low speeds. But at the higher speeds the wheels are full of energy and a warped rotor will show it.

Get the rotors resurfaced. It is cheep enough to have done. Hopefully they can have the warping ground out of them.