Whose baggage policies apply in the case of AA not getting your bags to QR? If AA, they would usually allow submission of receipts for reasonable expenses. I had no issue getting around $100 for necessities for 2 of us on a delayed bag from PHL-SRQ. That was only 1 day. I imagine you may be waiting more than a day so spend accordingly.
The Montreal convention applies in this case since it is an international journey
The airline is liable for up to XDR1288 (approx USD1740) for loss or delay to baggage
Should be able to go and purchase what is necessary until bags arrive
If having a decent travel insurance coverage, that may well be a quick and easy way to claim. My credit card will reimburse expenses charged to the card up to $800 at 6 hours delay with addutonal equal amounts at 24 and 48 hours.