A B757-200's R AFT EMER DOOR EICAS alerted after takeoff but the crew determined after completing the QRH that it was a false warning and with the cabin fully pressurized continued the filed destination.

Narrative

After a slight delay at the gate awaiting a fuel sheet; we taxied to [the] runway. Takeoff was normal with a 270 degree heading after departure. Level at 13;000 FT; the Captain noticed an R AFT EMER DOOR EICAS message. At that time; Center cleared us to a higher altitude. The Captain responded that we needed to stay at 13;000 FT to resolve an issue. I pulled my oxygen mask and draped it over my lap as a precaution. At that time; Center cleared us to maintain 13;000 FT. The Captain instructed me to fly the jet and talk to ATC while he retrieved the EMER DOOR - L (R) FWD (AFT) Irregular Checklist. At that point; both the Captain and I checked the pressurization panel to confirm that the aircraft was pressurizing. As a precaution; I suggested that we descend to 10;000 FT. The Captain agreed and asked ATC for 10;000 FT. We were cleared to 10;000 FT and handed off to Approach. Level at 10;000 FT; I was monitoring a developing line of thunderstorms that was west of our position while the Captain talked to Dispatch; Maintenance; and the First Flight Attendant. I also reminded the Captain that we had a uniformed pilot deadheading in the back if we needed his assistance. After the Captain completed the Irregular Checklist and confirming that the Aircraft was pressurizing normally; we both agreed that continuing to destination was safe; and in fact; the checklist permitted this course of action. The Captain informed Dispatch of the decision and I requested to continue the climb and to proceed on course with ATC. At that time; we were handed off to Center and continued to our filed destination. Dispatch also requested that we report the fuel over a mid route fix to confirm that the fuel burn wasn't adversely affected with our extended time at 10;000 FT. As it turns out; the fuel was sufficient and I believe that we blocked in with 7;100 LBS.