My 6mo is starting to sit unsupported but will frequently fall over and hit head on carpet. Is this potentially harmful if I allow it daily?

Relax. The brain is cushioned within the protective skull by layers of fluid and thin tissue. Tilting over from sitting height,especially on to carpet, does not create enough force to overcome babies built in protections.
Depends. Velocity and momentum will determine his overall fate. Gentle head bonks will be okay and not into the concussion concerns arena. Be proactive with safety and awareness/support in your infant who will indeed be more active/opinionated leading toward early toddlerhood in a few more months.