Not sure about age restrictions, but they need to be able to sit upright and support their own head to use the regular harness. Thule has a hammock-style sling seat for use with smaller kids.
Of note, the higher-performance trailer/joggers like the Cheetah and the Cougar come in single and 2-seater configurations. The single-seaters are lighter, but narrower. I had (just sold, actually) a Cougar-2 and it's W I D E; IIRC, it was almost 32" over the wheels. I got caught up once or twice (on trail and a pedal curb strike), and put the bike down, but didn't flip the trailer.