The floor is prob uneven under the carpet. I would NOT trust any tank/stand that rocks, however slightly. The sloshing water stresses the glass seams & might cause a leak down the road.
Carpets have a nailing stripe at the perimeter that holds it tight. That stripe is 1/4" up from the floor. If you rest your stand on it, you might get the rocking. It is usually 1/2" out from the wall & 1" wide, so if your tank is tight against the wall, pulling it out a bit might help.
Otherwise I would try shimming the stand so it is absolutely level. You would have to do that after filling, as you can't tell where the floor is until after the weight of the tank had compressed the carpet. that might involve multiple filling/unfilling of the tank.
You might want to shim with wilder pieces of plywood so the weight is spread over a larger area, or in the worse case scenario, put the whole stand on an oversized 3/4" plywood. <Would look ugly, tho!>
Wally stands are not too stable. If the stand itself is wobbly, rather than the stand rocking on the floor, then you might try to reinforce it on the inside.