It's within MCT for US at DCA and easily doable. Both MHT and CLT flights could arrive/depart from either Pier. There is a mini-bus running airside between the two Piers and it's about a 30-second ride. You should be at your CLT flight flight within 10 mins of stepping off your MHT flight.
Note that you do have to walk down/up stairs to get to the mini-bus, so make sure that your carryon(s) really are carryable.
If there's a serious delay, CLT is a US hub and there are lots of later flight options.