On the B737, during a 'dual channel' approach (i.e. an approach being made with both autopilots engaged), a press of a TOGA button will cause the aircraft to go-around and the autopilot / auto-throttle will remain engaged (i.e. the autopilot / auto-throttle will fly the go-around, all the pilots then have to do is raise the landing gear, and move the flap lever in order to accelerate the aircraft).
During a single channel approach (i.e. an approach made with just one autopilot engaged), a press of the TOGA button will cause the selected autopilot to disengage (along with an associated aural warning of such), it's then up to the pilots to action the go-around manoeuvre and all subsequent associated actions.
In flydubai 'dual-channel' approaches are not approved, wherein Cat II / Cat III (low visibility approaches & landings) are entirely hand-flown via use of the HGS / HUD... and accordingly it would be true to say that ALL landings in flydubai are hand-flown (i.e. use of 'auto-land' is not permitted) and therein at some point during an approach (regardless of it being either Cat I/II/III) the autopilot must be disconnected, and following which the remainder of the approach & landing (or go-around) is flown manually.
During a go-around, the normal procedure is to hand-fly the aircraft until the flaps are fully up and then to engage the autopilot... that said, some might (for workload reasons) engage an autopilot & auto-throttle once the aircraft is above the autopilot's 'minimum use height'.