I'd suggest upgrading to the towing package if you're going to make that
kind of trip.  We opted to do so in our minivan (1997 Plymouth Voyager).  
Otherwise we'd be too close to the edge of the towing capacity, and I
prefer a little margin just for safety's sake.

As for the desert driving issue, it depends on the time of year, also
the route you plan to take.  If you plan to go south, then west, that
means driving through TX, NM and AZ to get to the Grand Canyon.  Fairly
flat until you get into AZ where there's a not-too-bad climb to get to
Williams, AZ and the south rim of the Grand Canyon.  Can get to be
pretty warm across that stretch, also lots of miles between towns.  If
you plan to come down from Colorado/Utah to the north rim, then you're
talking about relatively steep grades and you'll definitely need the
towing package.