B732 FLC OVERSHOOT ASSIGNED DEP ALT OFF MDW BEING DISTR BY ACFT CONFIGNS.

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TAKING OFF RWY 22 IN MDW; BLEEDS OFF TKOF; WE WERE CLBING TO AN INITIAL ALT OF 3000 FT. WE CONFIGURED ON SCHEDULE AND CONTINUED HDG RWY HDG. PASSING THROUGH 2500 FT; I TOOK MY ATTN FROM THE CLB AND CONFIGURED THE BLEED AIR SYS. WE BOTH AGREE WE DID NOT HEAR OR RESPOND TO THE ALT ALERTER AT 2000 FT. WHEN I CAME DOWN FROM THE BLEED AIR PANEL; THE ALERTER SOUNDED THE 300 FT HIGH. I RESPONDED WE WERE CLRED TO 3000 FT. THE CAPT ARRESTED THE CLB AND DSNDED TO 3000 FT AND LEVELED OFF. SOME FACTORS CONTRIBUTING TO THE EVENT MAY BE: I HAVE BEEN AT COMPANY FOR 7 MONTHS; ONLY FLYING A FEW DASH 200'S AND NOT ANY IN THE PAST 2 MONTHS. CONFIGURING THE BLEED AIR; I WAS TAKING MY TIME SO AS TO NOT MAKE ANY ERRORS IN RECONFIGURING AND MAY HAVE DRAWN THE ATTN OF THE CAPT. WE WERE NOT SENT TO APCH UNTIL AFTER THE EVENT; WHICH IS UNUSUAL FOR MDW. NO COMMENTS WERE MADE BY APCH OR TWR AND WE CONTINUED WITH NO FURTHER ACTIONS. THE CAPT AND I DISCUSSED THE EVENT AND WORKED OUT WHAT WE DID AND HOW WE COULD HAVE PREVENTED THE OCCURRENCE. SUPPLEMENTAL INFO FROM ACN 498821: AT THE TIME OF THE ALTDEV; I WAS DIRECTING FO IN PROPER PROCS AND INSTRUCTING HIM TO SWITCH FREQ TO DEP CTL. CLBED TO 3700 FT EXCEEDING THE 3000 FT ALT LIMIT.