Thank you for your question.  Rosemary is a wonderful herb.  I use it often in cooking.  Because it is a woody herb, it can't simply be dug and divided as you would a perennial.  But it can be successfully propagated by either layering or taking cuttings.  

Propagate rosemary by layering in the summer.  Strip the leaves from 6 inches to a foot of a low-growing stem, leaving 4 inches of growth at the tip.  Bury it in a trench a few inches deep after scratching a  bit of the bark off and pinning the stripped area into the soil with a few bent wires.  Leave that 4 inch tip out to grow.  Water well and keep the soil moist.  The stem should produce roots in a month.  You could try this method now.   I have successfully rooted lavendar by scratching the bark off a stem and nestling into a bit of soil held firm with a brick or rock. 


Take 3-inch cuttings from rosemary in early to mid-summers.  Trim below a node (the bump where leaves join the stem) and strip off the bottom inch of foliage.  Dust with rooting hormone (optional) and put in moist potting medium in a pot. Tent with a plastic bag and put in a warm (68 degrees or so) area with bright light (not direct sun).  Take the bag off if excess moisture forms.  Roots form in 4 to 8 weeks. 

I hope this is helpful.  Good luck with your rosemary.