The best way I've found to hang rugs, square or otherwise, and what we use in the shop to display our hooked pieces, is by using carpet strips. These are the strips of wood that grip and hold a broadloom against the wall. Hardware stores sell them and most carpets stores would as well.
They come with short sharp nails that point upward at an angle that grab the rug and hold it tight. There are nails in the back to pound into the wall and if you have nice straight walls with new gyprock they can be used as is, but if you have old plaster walls the wood strip is rigid so nails won't hold on an uneven surface and the strip will spring off on one side. To fix this, you can take out the nails meant to be pounded into the wall and replace them with gyprock screws.
If using the nails to secure the strip to the wall, tap them in evenly by going back and forth the strip until they are all in the wall.
When hanging a half moon or round style rug you will need to use more than one carpet strip. A smaller one on the top where the curve of the rug is and a larger one at the base or if it is round somewhere in the middle. If round, you can always position a third piece closer to the bottom curve. Of course hanging square or rectangle rugs you only need to apply one strip to the top area unless the rug is large and weighty, then you should position one in the center to help support the weight.
These nails will not harm your rug but I do suggest positioning the hooked area on them, not the rug binding as it will pick it. Be careful removing the rug. Lift it upward so those nails don't grab on the loop backs and pull out wool. Of course if that happens you just hook it back in.
This technique will hold the rug beautifully and keep it from pealing off. Carpet strips are great in that you can take the rug down quickly to give it a shake to remove dust or show it off to your friends and then just as quickly, slap it back on the wall.
A small warning, handling these strips is like holding a porcupine so take care when attaching them to the wall.