American normally does NOT preboard children in coach, just First Class, the disabled and people with elite FF status. Having the carseat with you makes no difference in that respect. However, it is *sometimes* possible to get the carseat on board without having to carry it yourself, though it takes a bit of begging. Your odds are about 60/40, but I find it worth the effort if it works.
While you are sitting there waiting, watch the door to the gate.
At some point, there will begin to be uniformed people who go back and forth out of that door; this will be after the plane arrives at the gate, but well before they call boarding for your flight (which they will do about 30 minutes before scheduled departure.) That's your cue, as long as there is no one else standing in line at the gate counter. Take your carseat up to the gate counter, and VERY politely and apologetically, tell the agent that you are concerned about getting the seat onboard without hitting any other passengers, as you'll have your hands full. If the agent looks receptive, ask if there might be a possibility that someone could just take the seat onto the plane and set it down for you in your child's assigned seat. Tell the agent that you understand that no one can buckle it in for you, but that you would feel so much better not having to run the risk of hitting any of the first class passengers with it as you go down the aisle. If the gate agent is inclined to help you, he/she may call over one of the people who are going in and out of the jetway, and ask that person to drop the carseat in your seat for you. Usually they will agree to do it; you just need to show them your boarding pass.
If you manage to accomplish that, set yourself up as follows: you take the hand luggage and the stroller, and leave your travel companion with the baby. (Make sure that the baby knows that your are NOT leaving without him; they will sometimes throw a fit if Mom goes through that door when they don't. Hide and seek is a good way to describe what will happen.) You board as soon as your row is called, but your companion will hang back until nearly everyone else has started down the jetway. That should give you enough time to stow the carryons and install the seat. If you can't get the seat on board ahead, take the seat, the smallest carryon and the stroller, and roll down the jetway, pausing to fold the stroller and leave it at the end of the ramp. (You don't want to delay sending the stroller down until the last minute if you can help it; it could be left behind that way.)
