How long will it take me to get from the VAA flight that arrives in Terminal 3 E-gate, to my American Airlines connection leaving from Terminal 1 D-gate, same afternoon?
As with any US airport, leaving anything less than 2 hours is risky when transferring off an international flight.
You'll need to clear immigration, collect your luggage, clear customs, recheck your luggage and get to T1.
You might be lucky if the VS flight's early and immigration's empty. And there's a fast shuttle train direct from T3 to the D concourse. But if VS are late and there's a long queue you're in trouble. Better safe than sorry.