I thought maybe that was the case too, but later in the piece there is a marking of 'tre corde', which I thought means the damper pedal. Maybe I'm wrong?
Yep. Tre Corde means lift the una corda pedal off (literally means "three strings", ie, normal).
The pedal markings (Ped *, or ---^---^---) will be for the damper pedal.
Incidentally, if you are playing on an upright, the una corda pedal doesn't work the same as on a grand, so it's use is pretty much not going to achieve the effect that the composer intended.