No need for your EAD card, it might be a hassle and $ to get a new one if you lose it.
I've been out of the country twice on AP and all i brought were my AP letters, passport. I did also have proof of my reason to leave the country (work) just in case there were questions but that was never asked during my entry into the US.
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OCT 4th 2012 - DACA approved;
OCT 11th - SSN;
OCT 15th - License;
OCT 25th - First CC approved ///
JUN 6th 2014 - Renewal sent;
SEP 5th - Renewal approved! ///
APR 24th 2016 - 2nd Renewal Sent;
AUG 8th - 2nd Renewal approved