flying for a charity

I've tried to follow the "charitable airlift" discussions here over the
years and it usually makes my head hurt. I was just contacted with a
request to transport and I could really use some Usenet-level advice.
(Yeah, I've got AOPA legal services but I get better info here.)

There's a Rottweiler who was found in New Orleans and still needs an
oxygen tent. The request is to transport her to MSU from LSU. I'm
still working on justifying expending so many resources on this dog but
I might be in the area transporting another dog so I'm trying to gather
my thoughts and information.

I'd like to have the people involved pay the flight expenses. The
money doesn't need to go to me though. I'd rather see it go to one of
more of the rescue organizations I support.

I don't think this qualifies as a "charitable airlift" event. Also,
because there are no people being transported and there's no commercial
value in the cargo, it shouldn't be commercial, right? Except it is
for "compensation" (recalling the "even flight time is compensation"
threads). So what are the limits on having someone donate directly to
a charity as a result of the flight?

So far I've found this.
http://en.wikipedia.org/wiki/Pilot_c..._United_States

Furthermore, donations to a charity in exchange for flight is
permitted.

Anything else I should consider? I'm a little hurried and not able to
do as much research as I'd like right now.

Thank you!

--kyler