HDG TRACK DEV IN A NON ADHERENCE TO ATC CLRNC INSTRUCTION ON DEP PROC. RADAR VECTORING.

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ON THE ABOVE DATE I WAS THE FO AND PF ON A FLT FROM EYW TO MIA. IT WAS OUR FIRST FLT OF THE DAY ON THE 4TH DAY OF A 4-DAY TRIP. WE BOARDED OUR PAX AND AFTER A NORMAL ENGS START; TAXIED TO RWY 9 AT EYW. JUST AFTER SWITCHING TO THE TWR FREQ; THE TWR INFORMED US THAT OUR COMPANY OPS PEOPLE NEEDED TO SPEAK WITH US. DURING THIS TIME WE CAME TO A STOP AT THE APCH END OF RWY 9. I WENT OFF TO TALK TO THE COMPANY AND WAS TOLD THAT WE HAD A TPA PAX ON BOARD BY MISTAKE AND THEY WOULD RE-BOOK HER THROUGH MIA IF SHE WANTED. I INFORMED THE CAPT OF THE SIT AND HE GOT ON THE CABIN INTERPHONE AND INFORMED THE FLT ATTENDANT WHO WENT TO FIND THE PAX AND DISCUSS IT. MEANWHILE IN THE TIME TAKEN BY THE FLT ATTENDANT THE CAPT COMPLETED THE TAXI CHKS WHICH INCLUDED A REVIEW OF THE CLRNC (AS FILED; WHICH NORMALLY INCLUDED A L TURNOUT TO INTERCEPT V157 NE OF THE FIELD) AND MY BRIEFING AS PF IN THE EVENT OF A PROB. AFTER V1 WE WOULD MAKE A L TURNOUT AND PROCEED VISUALLY BACK TO RWY 9. I INFORMED THE TWR THAT WE WERE READY FOR TKOF AND THEY CLRED US FOR TKOF; FLY RWY HDG. TKOF WAS NORMAL AND AT 400 FT AGL THE CAPT SAID 'CLR L' AND I STARTED A SLOW TURN TO THE L JUST PLAIN FORGETTING THE TWR INSTRUCTION. AT THE SAME TIME TWR SAID CONTACT DEP WHICH THE CAPT DID RIGHT AWAY. (DEP IS NAVY KEY WEST.) THEY ASKED TO FLY A 070 DEG HDG FOR TFC TO THE N OF US INBOUND TO EYW. I WAS AT A 055 DEG HDG WHEN THIS INSTRUCTION WAS GIVEN AND PROMPTLY TURNED TO 070 DEGS. THE TFC WAS AN MLT AT OUR 9 O'CLOCK POS AND 3 MI. I COULD SEE THE TFC JUST STARTING TO FADE INTO MY TCASII SCREEN AT ABOUT THE 8:30 POS AND SHORTLY THEREAFTER PASS OFF THE SCREEN. JUST AFTER THIS DEP ASKED US IF WE HAD BEEN ASSIGNED RWY HDG BY THE TWR AND WE REPLIED THAT WE HAD. HE DID NOT ADMONISH US AT ALL AND WE NEVER GOT AN RA OR A TA FROM OUR TCASII UNIT. HE THEN HANDED US OFF TO ZMA. IN RETROSPECT; I THINK THAT ONCE AN AIRPLANE LEAVES THE GATE THE ONLY COM SHOULD BE WITH ATC UNTIL AFTER TKOF AND AREA DEP. SAME THING WITH AFTER LNDG AND GATE ARR; UNLESS IT HAS SOMETHING TO DO WITH THE SAFETY OF FLT. ALSO; OUR TKOF BRIEFING WAS FULL OF L TURNS AND WHEN THE CAPT MISTAKENLY SAID 'CLR L' I MISTAKENLY BLANKED OUT THE TWR INSTRUCTION AND STARTED MY TURN. THERE WAS NO TFC CONFLICT BUT THE POTENTIAL WAS THERE.