I am traveling on American Airlines to EZE with an arrival time of 7:30 am and a departing time of 11:35 from AEP. Suggestions on if I am going to make it and what I can do in advance if anything to expedite my travel between the two airports.
There are a range of options to get into town (Manuel Tienda Leon - a shuttle company, local buses or taxi) - see the piece on Wikitravel.
EZE is about 30-45 min from downtown by taxi, although during busy times it can be longer.
From town to AEP, it's easier - about 20 minutes by taxi.
Your best bet given your tight time-frame is to get a taxi from one to the other. They're not too expensive, and are certainly fast. White-knuckle fast.
edit - it looks like Tienda Leon does do inter-airport shuttles. If you're on time, you could consider them when you arrive. There's a guy usually waving a sign for them as you exit the secure area at the airport.
edit again - Driving time is approximately 38 min for 39km from airport to airport, according to Google Maps. Of course, that's assuming decent traffic.