A.M.
I would teach her to use the stairs going both up and down. But for the times when you can't be at her side, for safety's sake, install a child gate and the top and bottom so she can't experiment on here own. There's nothing wronge or stange about her wanting to go up and down the way she sees everyone else do it. She probably has very good cooridination do even do one stair. My 16 month old goes up but has never tried going down, probably because of the gates. I still carry him down and maybe now I will think about changing that.
Definitly get a gate. Finding her one stair down and proud of herself is nice, but scary. I would hate to find her at the bottom!! Crying from a fall!!!