^^You should be fine. I have traveled on different airlines via one ticket several times before and it's been fine (I even did three different airlines one time over to Asia - Air Canada, Korean Air and Thai Air - all Star Alliance airlines) and my bags always made it - checked all the way through. It's quite common now so as long as you protect yourself as Mike suggests, I wouldn't worry too much.
Also, when you are looking at American's baggage allowance make sure you look at the international allowance not domestic as you are on an international itinerary - you should be allowed two checked bags up to 50 pounds a piece...if you need more than that......'nuff said
Also, when I was in Oz a few years ago, I was flying home, and my itinerary went from Cairns to Sydney on Quantas and Sydney to San Francisco on United. They are not technically partners and I booked the tickets separately. I fully expected to have to pick up my bags in Sydney and re-check them on United but Quantas offered to transfer them to United for me (and I think they gave me boarding passes too somehow) and it worked out fine. I was very impressed with Quantas that they offered that - they must have had some arrangement with United just in Australia or something.
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