Air carrier First Officer reported executing a go-around after receiving a low altitude alert from ATC on a night visual approach to BHM.

Narrative

Going into BHM I was the Pilot Monitoring. Weather conditions were clear; but winds were gusty; making for a bumpy ride in the descent. After I obtained the ATIS; the Captain and I planned and briefed for the Visual 24; backed up with the ILS. Winds were 320@11 and runways 24 and 36 were in use at the airport. The altimeter setting was 30.18.Upon contacting Approach; we found out the current winds were 330@16 with gusts of 28 kts. We discussed the winds and determined we were getting close; but still within limits of landing Runway 24. Around leveling off at 3000 ft.; Approach informed us that the winds had shifted to 350@15 G25 and that they were now landing runways 06 and 36. We opted for the Visual 36 since the winds were favoring that runway and we already had the landing data.We briefed and discussed the particular threats for the Visual 36; which was going to be backed up with the RNAV 36. Along with it being a night landing; we recognized we would not have a GS and PAPI; and we were aware that BHM has surrounding terrain which can pose a hazard. When Approach offered to give us vectors for a 10 mile final for 36; we gladly accepted to help eliminate the terrain risk and set up for a stabilized approach.We were vectored in to intercept the final prior to IMOBY. Once cleared for the Visual 36; we descended to the crossing altitude of 2800 ft. The next waypoint on the approach was BERFY; which was the FAF and had a crossing altitude of 2300 ft. We crossed that waypoint on profile; set the DDA altitude; and continued down at 800fpm. Right after the 1;000 ft. call out; the GRD PROX switch light illuminated. We might have been slightly below snowflake; but seemed on profile. We did not get any aural warnings. Around the same time; Tower informed us of a low altitude alert. At that point the Captain initiated a go-around. Once stabilized; we set up the approach; and landed Runway 06 with no further issues.