I have no experience of that situation. Even if someone has, it might not extend to all outstations/agents/cases.
But I would advise that you pack a cabin bag for the night.
Your ticket is a through ticket, so they are likely to be required to check bag through. Whether it is a 20h or 26h transit, they will send the bags to a holding area anyway.
You might request to get your bags in DOH and they might (or not) obliged, but it and it will be big hassle. You won't be able to check them 24h early on AA, so will have to carry them during the day.

Another suggestion is to take advantage of the schedule change to ask for a change of flight allowing for a shorter transit in DOH. It seems that you want to do a stopover in DOH, but is it really worth it?