EMB-175 Captain reported getting an aural obstacle alert while descending on visual approach. The flight crew climbed back up to altitude and continued the approach to landing. Reporter cited a short flight and task saturation contributed to accepting the visual approach before being ready.

Narrative

Hot temperatures and thunderstorms in ZZZ2 required us to have a very quick flight from ZZZ-ZZZ1 for a fuel stop. We were cleared to the initial approach fix for the RNAV XX. As we approached the fix I realized that the vertical NAV was still thinking we were climbing to a higher altitude (an issue with TOC and TOD). I asked the PM to reload the approach and try and fix the issue. As we got closer; ZZZ approach asked if we had the field? We said we did and they cleared us for the visual approach to [Runway] XX. Not having a clear glide path I clicked off the guidance and automation and proceeded to fly the visual approach. We were still high and I pitched down to get back on the slope; we were then alerted to an aural obstacle caution message. For the dock cranes along the approach path. I added power and climbed back up. We were well clear of the obstacles and back on vertical path we continued the visual to land Runway XX with no further incident. The flight was only 10 minutes long. We were task saturated and while I tried to slow down and configure early; it was not enough and I should have delayed starting the approach. We discussed and decided that we needed to spend more time on the ground in ZZZ briefing and setting up everything we can for the quick flight to ZZZ1. Including briefing the full approach and getting landing numbers before we take off. So that we are not task saturated. I felt pressured to accept the visual approach when I should have asked for delay vectors. And lastly we should have gone around when we got the obstacle warning; that would have been the safest option at that point.