Depending on your kid size and the size of your trailer, they can ride in the trailer until they are 9. Not the most comfortable for them or you but it is possible. I have pulled an 11 and 8 year old (short distance but they did want to squeeze in to try it). Your 7300 should handle the load fine. I would only give extra caution if your seatpost is carbon fiber and then just check that the connector has no burrs and don't overtighten (I think the gators attach to the seatpost and not the seat). You should have no problems with that setup.
For me, we start cycling them out of the trailer about 5. I am "forcing" my 7 year old to ride solo this weekend on a 30 mile ride. Although I have told him he can go in the trailer or in the tandem position (lash his bike to the trailer) if he gets too tired.
Each kid is different though. My 6 year old does not have much interest in riding on their own but riding on the tandem or the tag-along is very exciting. Meanwhile, the 3 year old wants to ride the 6 year olds bike. In the end, I just want them outside doing something, and that is being accomplished.