I have the same Mac Mini 2009 connected, using the same HDMI adapter, to a Sony VPL-VW100 (1980x1080@60Hz).
It works fine.
First make the following checks :
1) connect directly, bypassing your AVR-2112CI, the Mac Mini to your projector
2) power-on first the projector
3) start the Mini
If this works, it means your AVR is the problem. Likely, your projector EDID does not come back to the Mini properly through it.
If this does not work, it means your 1280x960...