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.
I´m in the business of doing airport transfers here, this is a tight, but doable connection, and we suggest you get to AEP the fastest way you can, which would be to hire a reliable private chauffeured car service, who will be waiting for you with a sign right as you arrive. 4 hours is the bare minimum we suggest for this transfer, as your arriving flight may be delayed, immigration and customs can often take 90 minutes for morning arrivals, and if there is traffic, it can take 90 minutes for the transfer and AEP suggests that you arrive 90 minutes before a domestic flight.