I like the chariot series of trailers the best, but I don't know about height.
At 6 years, most people are doing a combination of "trail a bike" attached to an adult, riding their own bike, or switching to family walks while the 6 y.o, is on a push scooter and the youngest is in a backpack or stroller. I found that we slowed down a lot for the little cyclist for these years, and literally stopped to smell the daisies a lot more, and it was just as nice as the 100% biking to destinations we did before.
Note, the trail a bike was great because their stamina did not matter, and I could control their movement exactly while riding near traffic and intersections, saving them riding their own bike for quiet park areas or local side streets.