Can a dryer fit in a Chrysler PT Cruiser?

Depends on how big the dryer is. Measure the dryer and measure the Cruiser: do the math.

Dryers are not the same size. You will not be able to haul it upright, it must be hauled laying down and this can cause damage to the dryer itself, like drum rollers, heating element, drive system, some of the newer ones have load sensors and that could foul them up. Rent a pickup or large cargo van, something bigger or have it delivered.

GA is right, rent a pickup or truck to haul it.