Air carrier First Officer reported an altitude deviation during a visual approach to DRO airport resulting in a CFTT event. The crew disconnected the autopilot; initiated a climb and continued with the approach and landing.

Narrative

We were cleared for the visual approach into DRO. PF set the aircraft up to enter a left base for Runway 21. We began to configure about 10 NM out. As we got closer and began to descend we determined we were too close to the runway and opted to turn into a brief downwind to provide more room before turning in. During this time the descent continued and we got below 8;000 ft. The FAF on the RNAV is 8;800 ft.; so as we neared that point and began to turn in towards the runway we got an EGPWS caution terrain audio message. Just prior to getting the caution message I noticed we were not at the prescribed altitude for the instrument procedure and then the caution message went off; I informed the PF that the nearest prescribed altitude which was 8;800 ft. PF followed procedure and disconnected the autopilot; began to climb back up to 8;800 and continue turn towards the runway. The rest of the approach was uneventful.Cause: Lack of situational awareness in regards to our altitude and terrain; a possible miscommunication on what altitude we should be at when we decided to extend the approach to provide more maneuvering room.Suggestions: Next time I would opt to do the straight in RNAV approach allowing time to not only slow and configure and have positive course guidance and altitudes to follow. Another suggestion is for both of us to be more aware of preassigned altitudes such as an FAF or step down fix even if we are on a visual approach. This can be mitigated through briefings and continued CRM by both pilots.