Wobbly power steering pulley,belt comes right off.
With no information on the make and model of your vehicle, the information we can give you may or may not pertain to your vehicle. On most make and models, yes you can swap out the pulley by itself. You should ask yourself why the pulley has failed.
If the pulley was damaged or dirty, then you are most likely ok to change just the pulley. The pump may have failed or be leaking as well. If the pump was leaking onto the pulley, the buildup would cause the pulley to fail. Do you have an auto tensioner on the system? This component should keep the slack tight on the pulley. You will want to make sure the tensioner is working as well.
I recommend having a certified mechanic, such as one from YourMechanic, come to your location to determine if a power steering pump replacement is necessary.