The VGA likely is the issue. Not sure you can do 2550×1440 with a VGA cable. VGA is analog also and not the best connection.
From what I can see from the specs for a Q2577PWQ it has a DisplayPort socket. Just use a straight DisplayPort cable from the Mac Mini to monitor. No adapters (or maybe mini DisplayPort to normal DisplayPort for the Mac Mini).
DisplayPort to DVI might work, but as the monitor has DisplayPort anyway, you don’t need it.
Also, Mac Mini’s come with HDMI ports I think? Could just do HDMI to HDMI on the monitor. Though not sure if it will do the resolution.