A LR45 ON THE TEB DALTON DEP CLBED 3000 FT INSTEAD OF 1300 FT AS CLRED BECAUSE OF A MISSED TKOF BRIEF. ATC CLRED THEM TO 3000 FT WITHOUT COMMENT.

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AFTER DE-ICING ACFT; WE ASKED FOR TAXI CLRNC. THE GND CTLR ASSIGNED US RWY 19 WITH THE DALTON DEP PROC INSTEAD OF THE TEB 5; WHICH WE WERE ORIGINALLY ASSIGNED. HE ALSO STATED THAT RWY 24 WAS NOW CLOSED. WITH THE ORIGINAL CLRNC; WE WERE ASSIGNED 3000 FT FOR THE INITIAL ALTITUDE. WHILE TAXIING OUT; THE TOWER CLRED US FOR TAKEOFF BEFORE WE REACHED THE END AND WE TOLD THE TOWER WE NEED MORE TIME. I THEN REVIEWED THE PROC AND BRIEFED THE CAPT. ON CONTACT WITH DEP; I READ OUR CURRENT ALTITUDE AND ALTITUDE CLBING TO WHICH WAS 3000 FT. WHEN DEP RESPONDED; SHE SAID SOMETHING ABOUT VFR AND RESUME NORMAL SPEED. I READ BACK RESUME NORMAL SPEED AND BEING UNSURE ABOUT WHAT ELSE SHE SAID; I ALSO READ BACK 3000 FT. SHE THEN RESPONDED MAINTAIN 3000 FT. SHE ALSO STATED THAT SHE NEVER ASSIGNED US 3000 FT PREVIOUSLY AND THAT I READ IT BACK WITHOUT BEING ASSIGNED THAT ALTITUDE. I NOW REALIZE THAT I GOT 3000 FT FROM THE ORIGINAL CLRNC. UPON RECEIVING THE DALTON DEP; WE WERE SUPPOSED TO MAINTAIN 1300 FT AND MAINTAIN VFR. THE CAPT AND I BOTH THINK WE WERE BELOW 1300 FT WHEN SHE ASSIGNED US 3000 FT. NOT SURE AN EVENT OCCURRED. WITHOUT THE FURTHER CLB CLRNC TO 3000 FT; AN EVENT WOULD HAVE OCCURRED. THE ATC CTLR TOLD US TO BETTER REVIEW THE PROC. MISUNDERSTANDING THE DEP PROC ALTITUDE. BRIEFING THE CAPT THE WRONG ALTITUDE WHILE HE WAS TAXIING IN THE DARK. BEING PRESSED FOR TIME; CAPT DID NOT REVIEW THE CHART AND VERIFY THE ALTITUDE. BETTER REVIEW OF THE PROC. BE MORE VIGILANT WHEN THERE ARE LAST MINUTE CHANGES.