LIT Air Carrier departure experienced a TCAS RA event immediately after take off with reported VFR traffic that was maintaining visual separation; the reporter noting ATC should have delayed their take off clearance.

Narrative

This report is submitted to highlight what I believe to be an ATC error. LIT Tower cleared us for takeoff on 22R with an assigned heading. Immediately after take off; VFR; another carrier; traffic was called at our 1 o'clock. I responded that we were looking for traffic. Due to sun in our eyes; we could not visually acquire the traffic. ATC said the traffic had us in sight. Very shortly after the flaps were up; we got a TCAS RA to descend. We complied in accordance with FOM guidance. The last readout I saw on the TCAS display was +300. Almost immediately after we began the descent to comply with the RA; we began to receive a GPWS 'don't sink'. We continued to comply with the RA while noting our AGL altitude of about 800 FT AGL. The Captain and I agreed to continue to comply with the RA and that we would monitor our AGL altitude. Once clear of conflict; we continued to climb out. When told to contact Departure; I told the Tower that we had descended to comply with a RA for the VFR traffic. They responded; 'Roger; contact Departure'. We never should have been cleared for take off with VFR traffic in a position to give us a RA. A delay of a minute would have completely eliminated this unsafe condition.