I would be surprised if any jet operator would land on a dirt strip unless the aircraft was certified to be able to operate from one. The main dangers I can think of include FOD damage to both engines from gravel injestion as well as damage to the underside of the wings, fuselage, flaps, gear doors etc. from gravel rash.
I seem to recall that Boeing had a special mod kit for the older B737 for gravel runways. It had bleed air jets to break up engine vortices, a cover to prevent the nose gear from spraying gravel everywhere, and fibreglass armour for the underside of the flaps.
Then of course there is the pavement strength question.
You might find it quicker and cheaper to locate one of these aircraft and charter it, or switch to an RAAF Hercules or Caribou.
Anyway I'm only an amateur, the professionals may have better advice.
P.S. If you find one, tell us ppruners so that we can come and watch
