Your health insurance pays for your medical bills, but what about your other monthly expenses in the event that you are unable to work due to a disability? Disability insurance is meant to be a wage replacement in such cases where you cannot work due to a disability. An individual disability policy will typically pay you sixty percent (60%) to seventy percent (70%) of your monthly earnings leading up to the onset of your disability. You can purchase coverage that will cover you so long as you cannot perform the substantial duties of your own individual job, and you can buy coverage that will cover you for two (2) years, five (5) years, or until retirement age (typically age 65).
So the answer is Yes, you should buy as much coverage as you can.