Rosemary is easily propagated. Put several clippings (new growth that has green stems, not the brown stems) in a pot with a 50/50 mix of perlite and vermiculite, cover with plastic (I use a 2 liter clear plastic pop bottle with the bottom cut off and the cap still on), keep damp but not soggy. When the rosemary develops roots put in a pot with potting mix and keep damp, but not soggy.
Mint can be rooted easily by simply fastening a branch down into the soil with either a stone or upside-down U shaped wire, and when the roots are established, cut the new plant from the old branch and plant.
Cats go for nepetia, aka catnip, but don't usually dig in spearmint, peppermint, or any of the other mints.