My 2007 had that same "thump" and after awhile, my steering wheel would shake/vibrate every time I braked from a speed of 30mph+ I took it to a brake shop and they said the rotors were bad, they replaced the rotors and everything was fine for awhile. About 3-4k miles later, the thump came back, and pretty soon, so did the braking shake/vibration. I soon decided to replace the brake pads and inspect the rotors, which looked fine. I put the new brake pads in and reassembled the front wheels. Once again, everything was fine for awhile. The noises and vibrations came back, but I didn't get in a big hurry because I'd never seen any real problems so far. About a week later, my right front wheel sounded almost evil and the steering felt like I was in a rodeo. Luckily I was just a few blocks from home, so i limped it to my garage. While the car cooled I researched "front-end problems with HHR," apparently they are notorious for such issues. However, when I jack up the right front end, the lug bolts had all loosened by at least 1/8inch, so the wheel was just wobbling on it's bolts. The wheel was trying to wobble itself off the car. I was able to put band-aid on it, but I noticed that the holes in that wheel are a little too big for the post/bolts that the wheel is supposed to be bolted onto with lug nuts. My HHR may have some other problems beyond that, but the loose wheel may certainly explain both the "thump" when going over a speed bump and the shaking when i brake. I have the standard cheap wheels made for hubcaps.(But now planning to buy some higher quality wheels)
If you're experiencing any issues I've described, please jack up your car and make sure your wheels are on tight. If I'd waiting another week or two to check mine, I might very well have been seriously injured, killed or even worse, I could have caused an accident that hurt or killed others