We have an old-school red metal Radio Flyer tricycle and my 18 month old son loves it. He can't reach the pedals quite yet, but he can get up on it (thanks to the two steps to get on the back) and he loves to hold on and be pushed. I can get on the back and pedal him around and it hasn't broken yet. :) It IS a little tippy, but moreso for my almost-5-yr-old, who careens around the driveway on it--it's really too small for him, and he wants to go too fast. We got a lot of use out of it and it's still in great shape.
Edit: We also have a Radio Flyer plastic thing that converts from Hot Wheels to tricycle. That one is neat for my older son (5) but he is just now able to pedal the hot wheels--it was a LOT harder for him to push in front of him than on top of the pedals. Anyway--the Radio Flyer thing that converts is neat; it's easy to switch around and also pretty heavy duty--but keep in mind the pedaling thing; depending on how your daughter is built, it might be easier to pedal a higher/lower/more-front pedal/more up-and-down pedal bike.