The vehicle is a "sociable" of European origins. The squared 90% corners, lack of curved lines, and strong "utilitarian" aspect are typical of the vehicles made and found on the continent. US and English vehicles tended to have rounded curves and more "flair" to their design. They also tended to accomodate 4 passengers in a back to back arrangement, or two seats facing forward, as the "sociable" or "vis-a-vis" (French for "face to face") wasn't one of the more popular vehicles in the US/England because they usually demanded a coachman.There were a few US vehicles made to be driven privately by the owner which featured dash seats, but those generally had small "foot stool" type seats that folded down when needed and were flipped up out of sight when not used.
In this vehicle pictured the driver sat in the seat facing the horses (this vehicle was designed for a pair BTW), and any guests sat either next to the driver, or in the back facing seat. It isn't a child's carriage, or designed specifically for children. It was designed simply to accomodate 4 passengers. And it wasn't a gender specific carriage - it could equally be used by a lady or a gentleman.
I'm not sure you'll find a date on the axle, hub, or wheel. You might, however, look under the seat, or on the body framing to see if a number is stamped there. Depending upon what you find, the CAA may be able to help you ascertain if the number is clue to one of the European carriage manufacturers.