I don't grow Rosemary and can not ever get it to really grow, So I can't offer any advice on this except: If it was me...I would wait until
spring and see if it sprouts back out. It is a tender perennial, so it is possible that it may not come back at all either way...What
zone are you in? If it sprouts back out then you could repot it, try to dig it up in a root ball (with as much dirt around the roots as possible)Until then I would place some sort of barricade around it to keep the puppies away from it & then just wait and see if it lives.