This is a tough one. Jenna was up and walking around furniture before 9m, and then walking at 10m. I think the biggest problem is when they are moving around so early, the really haven't got the understanding that if they aren't careful they may hurt themselves.
Jenna had lots of bumps and things, it was heartbreaking, but its completely normal I think.
Just get rid of all the pointy dangerous stuff in the room, and maybe try to limit her play area to where there is soft landings.

A toddler in my MG has just started walking (@18m) and because she is so sure of herself, she isn't falling over or getting any bumps. Its an age thing.

The worst one is where the teeth go through the flesh behind the lips! That is scary.