Air carrier First Officer reported descending below glide slope during approach and receiving a landing gear aural alert. Flight crew climbed back to safe altitude and continued approach.

Narrative

As we were on the ZZZZZX arrival we were given a vector to intercept the localizer for XXR; and we were cleared to decent to maintain 2500. I was on heading and decent mode not VPATH down to 2500; 210KTS. When I Heard we were cleared for the Approach; I mistakenly set the final approach fix altitude of 1600; thinking that there was a blocker altitude of 2500 that protected us as we continued our decent and intercepted the localizer. We were given 180 KTS or faster to a 5 mile final and I began slowing and asked for flaps 1; At the same time this was going queried the Captain to clean up the box so we would sequence properly on the approach; this caused us to be a bit task saturated with radio calls and FMS duties and configuration changes. We started to level off at 1600 ft outside of ZZZZZ1 and received the Landing Gear Aural Alert; when we realized what was going on; I set a higher altitude on the Altitude select window and commanded a climb using VS. at this point we were on the localizer inbound and started slowing down as well as fully configuring. We intercepted the glide-slope and continued to land.After we landed the Captain and I discussed the incident and realized the mistakes I had made. I should have not set the final approach fix altitude until I had verified that there was a VNAV protection Blocker altitude that was going to capture; in this case I dont believe that was the case since ZZZZZ1 was at 2800 and we were descending to 2500. In this case I should have ensured that I leveled off at 2500 VALT CAP before setting the final approach fix altitude. Secondly when we did receive the Landing gear aural alert; I should have initiated a go around instead of just setting a higher altitude and using VS to climb. Possible contributing factors; Expectation Bias of joining and intercepting the Localizer via ZZZZZ2; (IF) on the ILS XXR and ending point of the STAR. Having a bit better Guidance and less distractions setting up the FMS usually expecting they might clear us for the approach from that point. A bit of fatigue; I noticed I had hit a bit of a Circadian low about halfway through the flight with an XA:20 alarm early morning stormm deviations and a bit of a sit in ZZZ1.