FLC PERFORMS GAR; RECEIVES TCASII RA.

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FO WAS FLYING ACFT. WE WERE LESS THAN 500 FT ON SHORT FINAL. A HVY WAS JUST EXITING RWY 36R. WE WERE CLRED TO LAND ON RWY 36R. ACR Y JET WAS IN POS ON RWY 36R. HE WAS CLRED FOR TKOF. TWR ASKED IF WE COULD SIDESTEP TO RWY 36L. WE WERE TOO LOW AND I DECLINED. I TOLD TWR THAT WE WERE GOING AROUND. TWR DID NOT GIVE US A HDG. I ASKED FOR ONE BECAUSE I KNEW THAT ACR Y WAS JUST BELOW US. WE CONTINUED STRAIGHT AHEAD IN OUR GAR AND TWR TOLD US TO FLY 330 DEG HDG. WE FINISHED OUR CLEAN-UP AND FO STARTED THE L TURN. I ALSO HAD TO ASK FOR AN ALT AND WAS GIVEN 3000 FT. AS WE STARTED THE TURN; TCASII ALERTED US TO TFC. WE COMPLIED WITH THE RA. THE RA ENDED ALMOST IMMEDIATELY AND I NOTICED THAT; ACCORDING TO TCASII; ACR Y WAS APPROX 100 FT VERT SEPARATION FROM US AND AHEAD AND TO THE R ABOUT 1/2 MI. WE WERE VECTORED BACK FOR ANOTHER APCH AND LANDED UNEVENTFULLY ON RWY 36R. UPON ARR AT THE GATE; SEVERAL OF OUR RAMP PERSONNEL SAID THAT THEY WITNESSED THE ABOVE AND INDICATED THAT FROM THEIR PERSPECTIVE; THE WHOLE EVENT LOOKED VERY CLOSE. I WOULD ALSO ASSUME THAT PAX ON THE ACR Y JET MAY HAVE WITNESSED THE WHOLE EVENT. IT APPEARS THAT MCO TWR LCL CTL SHOULD PROBABLY NOT HAVE PUT ACR Y INTO POS ON RWY 36R. THEY ALSO SHOULD NOT HAVE ASKED US TO SIDESTEP WHEN WE WERE SO LOW. TWR DID NOT ASK US TO EXPEDITE OUR TURN DURING THE GAR; ALTHOUGH WE DID SO IN A TIMELY AND SAFE MANNER. ALSO; WE DID NOT HEAR MCO TWR TELL ACR Y TO TURN AWAY FROM US.