I started taking my son with me on rides starting at 9 months on a child seat. He out grew that at 13 months and I put him in a trailer, a Burly Cub. He absolutly loved it. We used to ride all over town with it (pathways only). Then I took the big chance and got him a tag-along (Adams Trail-a-Bike, folding type) when he turned 4 years. After some adjustment, he loves riding with me. We moved to another town without bike paths, but live in a quiet neighborhood and can ride for up to an hour without getting too bored. Sometimes we even venture down to a nearby state park and ride the light trails together just fine.
Take your time with her and kind of let her guide you on what she wants to ride. Consider her size and ability before jumping into something new like what you are currently doing with the Burly. Borrow or rent a tag-along so she can get used to one before buying one.