GND CONFLICT AT A NON TWR ARPT WHEN A DEP SH33 PERFORMS A TKOF WITH A G4 ON SHORT FINAL AT DTS.

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WE WERE DEPARTING DTS ON AN IFR CLRNC. AFTER ENG START-UP; I CALLED DESTIN TFC TO ADVISE WE WERE TAXIING TO RWY 14. THEN; WHILE MONITORING CTAF; I PICKED UP OUR CLRNC FROM EGLIN CLRNC ON 127.7. WHILE THE CAPT TAXIED THE ACFT; I COPIED OUR CLRNC; READ IT BACK; AND CALLED EGLIN DEP CTL; ADVISING THEM WE WERE #1 FOR DEP. WE THEN RECEIVED OUR RELEASE FROM EGLIN TO DEPART DTS ON RWY HDG UP TO 2000 FT; 'TFC PERMITTING.' ALL THE WHILE WE DID NOT HEAR ANY OTHER ACFT ON THE CTAF FREQ NOR OBSERVE ANY OTHER ACFT IN THE PATTERN. MY CAPT LATER TOLD ME HE OBSERVED A LEARJET POSITIONED AT THE OPPOSITE END OF THE RWY AND SO HE MADE AN ADDITIONAL CALL TO EGLIN DEP; ASKING THEM IF THEY HAD ANY OTHER ACFT RELEASED FROM DTS OTHER THAN US AT THAT TIME. THEY TOLD US THEY DID NOT. ALSO; MY CAPT STATED THAT HE OBSERVED AN ACFT IN THE DISTANCE WHICH APPEARED TO BE A DC9 ON APCH INTO OKALOOSA REGIONAL ARPT; A NEARBY ARPT WITH COMMERCIAL FLTS. THE ONLY OTHER TFC THAT EGLIN DEP ADVISED US OF WAS AN ACFT '1 MI N OF THE FIELD.' AFTER RECEIVING THIS INFO; I CALLED DTS CTAF AND ANNOUNCED THAT WE WERE TAKING THE ACTIVE RWY 14 FOR A STRAIGHT OUT DEP. HAVING OBSERVED NO OTHER TFC AND HEARING NO ONE ON THE CTAF FREQ; WE TAXIED ONTO THE RWY AND I BEGAN TO PUSH UP THE PWR LEVERS FOR TKOF PWR. THE CAPT (PNF AT THAT TIME); MADE THE 'LIGHTS; PROPS FUEL AND TIME;' CALL OUT AND WE BEGAN OUR TKOF ROLL. AS WE WERE APPROX 1/3 OF THE WAY DOWN THE RWY AND REACHING 70 KTS WE HEARD A GULFSTREAM CALL ON THE CTAF FREQ THAT HE WAS 'ALREADY ON SHORT FINAL' AND SOMETHING LIKE; 'YOU REALLY NEED TO BE LISTENING UP.' MY CAPT TRIED TO LOOK AROUND OVER HIS SHOULDER -- AND THEN ADVISED ME TO CONTINUE THE TKOF; WHICH I DID. MY CAPT XMITTED THAT IT WAS THE 'FIRST CALL THAT WE HAD HEARD' AND THAT 'YOU NEED TO TALK MORE!' MY CAPT ALSO STATED ON THE FREQ THAT WE WERE ALREADY ON THE TKOF ROLL AND WOULD BE WELL CLR BY THE TIME HE TOUCHED DOWN. THE GULFSTREAM PLT MADE ANOTHER COMMENT ABOUT WATCHING OUT FOR TFC AND SOMETHING ELSE ABOUT LISTENING TO THE FREQ. WE TOOK OFF WITHOUT ANY UNUSUAL PWR APPLICATIONS OR MANEUVERING. WE FOUND OUT LATER ON; THAT THE GULFSTREAM PLT HAD MADE SEVERAL CALLS EARLIER ON 122.8; THE OLD UNICOM/CTAF FREQ. I THINK THAT THE AMOUNT OF TFC AND TYPE OF JET ACFT THAT OPERATE FROM DTS ARPT; WARRANT THE OPENING OF AN ATC CTL TWR. JUST MY OPINION.