A BE1900 flight crew described encountering wake turbulence after takeoff from FLL; which distracted them from raising the gear.

Narrative

The following event occurred while on my last leg of the day. A 737 began its takeoff roll when ATC instructed us to position and hold. As we completed the runway check list; we were cleared for an 'immediate takeoff; left turn to 060; traffic on short final'. The 737 was just lifting off the runway. As we began our takeoff roll; I briefly cautioned the First Officer about the possible wake we may encounter after takeoff. Right after liftoff we began to encounter the jet's wake. I instinctively reached for the controls and instructed the First Officer to turn a little to the left and keep the positive climb attitude. He did as instructed and we exited the encounter within several hundred feet. I did not need to apply any input on the controls myself. First Officer asked for climb checks and I began the check list when ATC then told us to contact Departure and I acknowledged. I called Departure Control right away as I needed a turn to the north soon to avoid severe weather along the coastline. The rest of the enroute phase of the flight I worked the weather radar and coordinated with ATC for heading deviations. As we approached [destination]; the weather was good at the field; but a line of severe thunderstorms lay 10 miles to the east in a north - south line slowly approaching the airport. We were about 20 miles from the airport when we began to run the descent checks. During the approach briefing I suggested that we configure for the approach early and we discussed possible windshear from the approaching weather. We were 15 miles at 2;000 FT on the localizer for ILS Runway 6 when the First Officer asked for flaps 17. Speed check; 170 KTS; I selected the flaps and said indicating 17. At 1 dot above the glide slope; First Officer asked for gear down and I replied speed check 160 KTS and reached for the gear and found it already down with 3 green lights. My first reaction was did I select the gear too at the time we configured the flaps? We continued the approach and landing. On the ground we discussed the event and concluded that we may have missed the gear during the wake encounter. I called Maintenance Control and advised them of the situation. They sent a mechanic the next morning and inspected the gear and found no discrepancies and signed the aircraft to service.