I don't mean out in public, but like out in your back yard? I don't see a problem with it, my DD is 14 months and just beginning to walk and I don't think it's really necessary to put shoes on her all the time, especially when we're at home.
Anyway MIL keeps insisting that she has to wear shoes or she'll get bitten by ants. Fair enough, I worry about that too but I'm always supervising and if I notice ants I just move her away. What do you think?