A certain amount of rest after low back pain is normal and in some cases recommended. But if you rest too long, your back muscles will begin to weaken. This, of course, makes it harder to recover fully from low back pain.
A recent study looked at patients with low back pain who did an aerobics and stretching class twice a week. The class included a half-hour of exercises targeting the trunk and legs, with patients using their own body weight as resistance. After three months, these patients showed better back strength and endurance. In fact, they did as well on strength tests as other patients who were doing specialized back strengthening or getting one-on-one physical therapy.
Based on this study, a low-impact aerobics class with a special focus on strengthening the trunk and legs could do your back good. Your doctor can give you more specific advice, based on your history and condition.