How would we calculate the load factor on an aerial vehicle while landing due to sudden gust loads?
You need at least the stroke of the tire-gear combination to calculate a load. If the airship contacts the ground with a velocity of $w$ and a mass of $m$, the impulse $m\cdot w$ needs to be absorbed by a force $F$ acting along the stroke $s$, as in $m\cdot w = F\cdot s$. Adding airship flexibility will greatly improve the accuracy of the result, because I suspect the hull will deform easily and add to the stroke.

If you need an example of how this is calculated for a Boeing 747, please click here.