That sounds more to me like it's an engine running problem.
Typically the mount that causes the most problems is the front engine mount- or passenger side. That's the hydraulic mount. You have 3 mounts: the front, the transmission mount, and the torque-strut mount which is also called the lower/ dog bone mount.
I think my front mount went out very early, but I didn't replace it until much later in the car's life. I'm not upset by vibrations at stoplights. I just keep imagining myself as being in a hot rod- yeah, my 4 cyl shakes the car because of all that power! Anyway, go find your front mount, you'll see rubber surrounded by cast metal, with your finger push on the rubber part. It should feel solid. If it doesn't feel solid, then look for signs that the fluid leaked out- which if it doesn't feel solid, the fluid leaked out. That mount is toast if the rubber is not supported by fluid inside it like I described.
The lower dog bone mount is the one that you might hear go "thunk" if you floor the engine from a stop. That doesn't mean it's bad. It breaks several ways, but tends to be the most resilient of the mounts. The bracket that holds the mount to the engine can break. The rubber parts of the mount can wear out over time, and the bolts can rust in place making the eventual repair from normal use annoying. And yeah, rocks can get stuck between the mount and either of it's brackets causing vibrations.
The transmission mount is culprit #2 of vibrations. This one is solid rubber, but that solid rubber tears, and it can be manufactured out of spec so that the rubber part is too thin around the bolt. Imagine a flat piece of rubber bolted horizontally to the car body, then a bolt goes through the center of the rubber vertically, and then into the transmission to hold it in place. That's basically how that mount works. It is located underneath the battery bracket. To visually inspect that mount, the battery and it's bracket must be removed. If any cracks are spotted and verified to be cracks (not rubber left over from casting), then the mount must be replaced.
As far as what I think it probably is- engine running problems- how much do you know how to do, or want to do as far as maintenance on your vehicle? You have low mileage, but the car is old- 4 years now, and only 36k, so about 10k miles per year. That's great for keeping some things going, but it's hell on others. Mounts are one of those things that I feel should be least affected by time. I don't start looking for rubber decay on parts from age until closer to 10 years of age. However, it might be that your mounts sat on a shelf for 5 years before being used- that I don't know, and that's why I listed how to verify the mounts are good or bad for yourself.
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