Yes, keep exercising or start a program if you have not been exercising. However, you do need to make adjustments to lessen loads on the spine. In addition, improvement of balance and core strength along with quadriceps (front thigh) muscles is important for fall prevention. Regardless of your bone density, you probably will not break your arm, shoulder, or hip if you don’t fall.
The best way to proceed is to receive professional guidance and instruction. You need to learn how to move properly in performing your regular day-to-day activities as well as in your exercise routine.