There was a thread here about two weeks ago about a family that had 3 hours to connect from IAD (arriving on BA from LHR) to DCA (flying AA to MCO). The family did not have Global Entry and were not U.S. citizens. They made it in ample time - although it was a Saturday (Saturday before Christmas).
You're kind of doing the reverse, but you do not have to worry about Customs. You do however have to worry about baggage and traffic to IAD.
Your option is Shuttle from LGA to DCA which frequently is not a baggage heavy flight. You then have to get to IAD. You don't say what day of the week this is. If its a weekday, there is going to be traffic at 7:00 on I-66 - at least until the Dulles Toll Road (I'm assuming 30 minutes from deplaning to being out of the airport). I'm going to say 45 minutes from DCA to Dulles which puts you into Dulles at 7:45.
It should be enough, but its going to be tight especially if your DCA-LGA flight is late.
AA will NOT through check you bags. You must claim them at DCA and recheck them with AY at IAD.