I don't think it is too young to be walking at all - to me that is a silly comment. If you can walk, then you're old enough to walk.

But I must admit, I insist that DS holds my hand when he is walking (other than at the park). If he won't hold my hand then he goes in the pram. Personally i am a worry wart and know how quickly toddlers can get away. I'm mostly paranoid about roads, but when I'm at the shops I'm often distracted looking at things, so at least if he's holding my hand I always know exactly where he is.