What should I look for in a "trailer bike"/"tag-along" bike for a child? My daughter is growing fast, and will soon be too big for the child seat that is on the back of my bike.  She is not yet ready to ride on the road, so I am thinking of purchasing a "tag-along" bike.  What features should I look for, and are there anything to look out for?
Most of of trailer-bikes are pretty similar:


One speed. An inexperienced child will struggle to keep up when you pick up speed. She will also not be able to help much on the steep climbs.
No brakes. Your hands do a lot of work, and your stopping distance is longer.
BMX-style handlebar that can rock back and forth, as child size/shape changes
Attaches to tractor-bike's seat post. When you turn left, the trailer will lean right.
Flexy. As your kid gets heavier, this can make slowly climbing a steep hill really hard. You can't go straight.


I found that it was really good for teaching my son how to pedal, and build the appropriate muscles, so he was at an advantage on his own bike. 

The flex was not an issue when we started, but a couple years later I had to retire the trailer. I couldn't track a straight line up a hill. 

Some models have 5 speeds. That's more complexity, but if it breaks you can still get home. It can help a kid learn about shifting. 

The Burley Piccolo attaches to a special rack, making it lean properly in turns and supposedly reducing flex.

I used to hitch on a standard 2-wheel trailer to my tandem-trailer, either to carry groceries or to pull my baby twins. We had 5 wheels, 4 people, were 16' long, and weight 400+ lbs. I had to take corners carefully.