WE got DD this lovely little pushchair from Toys R Us for her 2st birthday (2 years ago). IT says from 3 years,, but the handle was adjustable - so it could be made lower for her to push. And it was very stable, unlike so many, so she couldn't pull it over on top of her.
Thankyou katemum - it was on her first birthday. On it you can see how the handle is put to the lowest position. She still uses it now - turned 3 in April. It has had almost daily use and is still in excellent condition. And bigger dolls do fit in it - DD's baby Annabel, Little Lucy and her Cabbage Patch thing all fit in it fine.
dd had a simple plastic Winnie the Pooh one, similar to the Ladybug one, (branded Lady Magic) from Argos, recommended age from 18 months. Think you can now get a similar style with Disney Princess and Mamas and Papas fabric like here but their site is slow today. The handle height adjusts and it converts to a cradle when they outgrow the pram. Do bear in mind that unless she is walking solidly by then it will be less stable to push than a normal pushalong walker and harder to manoeurve.