I would avoid the little light weight buggy types for now as they really aren't very stable, and often children this age tend to still lean forward and push down on the handles a bit too much - and then the buggies topple.
I bought my 1yo neice a pram from Toys R Us. It has an adjustable handle height, and was a it more sturdy - meaning it was much less likely to be pulled over or topple backwards. It was similar to this. Could be laid flat like a pram or the back/foot rest changed to be like a buggy. Baby doll faces them too which my neice liked.