As far as I know data you want is not available on SNMP.
3750#sh mls qos interface FastEthernet0/1 statistics
output queues dropped:
queue: threshold1 threshold2 threshold3
queue 0: 0 0 0
queue 1: 100989 0 0
queue 2: 0 0 0
queue 3: 0 0 0
What you'd like to know is ifIndex, queue, threshold and drop counter. I'm not aware of populated MIB/OID where these values can be polled from.
Like John Jensen explained, outDiscard is only thing you can get, but it aggregates all of this, so you won't know if it's BE, AF, EF, NC or what, which is dropping. You probably wouldn't care about BE drops, but you'd care about EF drops.
There are two OIDs where these aggregate egress drops are stored, if your ifIndex is 10001, you'd find them here (symbolic and numeric presentation):
3750/3560 are not very good switches for application which can microburst, i.e. if your egress is 1GE and ingresses are 1GE too, two very low average rate ingress ports can easily congest the egress port, causing drops. To maximize the available buffers (and minimize microburst drops) follow this document.