Becci, what direction are they facing right now? Mine is planted in the middle of my front yard in full day sunshine (its the SW corner of property, what I call "no mercy" zone). You typically find pussy willows growing in Wetlands, marshes or bogs, so keep that in mind when you relocate it.
I'd wait until it becomes dormant in the fall.
We transplanted ours from a pot (about 2ft lil twig) in the spring and it already had catkins. Now its 5 times the size! Also, if its near your lawn (that you fertilize) it may be getting too much nitrogen. Hope that helps. Let me know how it goes when u transplant.