Though 3.5 hours seems like enough time to transfer airports.. it's really cutting it pretty close.
A lot depends on what day you're arriving. Thursday-Sunday is notoriously bad for arrival/departures *AND* you're traveling between two of the most congested airports in the country, meaning arrival time in JFK is anybody's guess. Traffic from JFK to EWR can be bad as well. (It's not a pretty story, sorry)
Good news is, since you only have carry on, it's probably best to consider the train from JFK to EWR. There's a lot of changing lines (MTA,LIRR,PATH,NJ Transit) involved but, you'd avoid the car traffic. I don't know the exact route to do so, but a google search should point you in the right direction.
If price isn't an issue you might consider taking the
copter from JFK to EWR
Good Luck
CJ