The upper limit for the age of child you can take depends on the size/height of your child, and how much leg room the trailer has. Burley is said to have the most leg room, and they suggest 6yo as the upper limit. My older 2 children are small for age; won't be the size of the average 6yo until they're 7yo. But by 4-6yo, most children can use either a childback tandem or trailer bike or even ride on their own (my 5yo is riding half a mile to school now on his own bike, and he's the height of the average 4yo).
Our solution for ferrying a very small baby, and it's a common one, was to securely strap an infant carrier/small carseat into the trailer until the baby outgrows that, which is usually about 7-9 months old. This is criticised as having too little cushioning for the baby's head/brain against the shocks of the road, but my daughter is 3 now and I don't think she's any worse for it. The straps also aren't designed to hold a heavy car-seat and might break, but I guess depends how heavy your car seat is. We have found that our very little ones don't like to go (start crying) offroad with any set up, though if we were using a trailer without adjustable suspension, that might make the difference. From about 6 months old, baby can start riding in a seat behind the bike, or in our situation, from 7-8 months, we were wedging baby in the trailer next to an older sibling, using terry nappies as adjustable size booster seats. If the baby isn't comfortable he/she will cry to let you know. There is a problem of baby slipping down if you don't have some sort of make-shift booster seat until they get to the 12-18 month size. Alternatively, suitable for (I think) babies up to 3-4 months old, there is a Dutch contraption called Babybike.
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