Getting through southern Ohio and West Virginia and Virginia or going through Pennsylvania and down through Maryland will mean getting over some very big climbs so put a nice easy freewheel on there for that. Going downhill on a fixed gear is almost as bad as climbing. Definitely have brakes front and rear.
1000 miles in 14 days is over 71 miles a day. Certainly the guys from Gran Fondo that did RAAM on fixed gears could do it.
I could do it but it would be very tough. Some days well over a hundred miles, other days maybe 50.
Just yesterday we did a road ride that included a 1+ mile climb with an average grade of 9%. I was in my 34-24 gear(37 gi). On my fixed gear bike I could take a higher gear but not too much higher; maybe 34-17(52.5gi) at the most.