Hi Debra,
If you use Molasses you could certainly use white sugar instead of brown.
However...let's talk about the molasses. Would honey be an option for you over the cost of corn syrup? Honey may well be more expensive than corn syrup in Australia? I don't know the relative costs of these ingredients in Australia but, if honey is at all doable, I believe it would make a more satisfatory substitute for corn syrup than molasses for a couple of reasons: First, honey has a lower water content than molasses so it will give you a harder, firmer end-product (which is exactly what you want in construction-grade gingerbread). Secondly, molasses may be more difficult to work with from a color perspective, if that is at all a concern. (For example, If you are aiming for a particular shade of baked gingerbread or if you want to tint your unbaked gingerbread dough, it could be extremely difficult to do with a molasses-based formula).
Having said all of the above, I actually do think molasses would likely work okay and give you satisfactory results but honey would definately my first choice if you can use it. One last thought, If you are going to use molasses, consider increasing the flour by about 30-60 grams (2 to 4 tablespoons) per batch of dough to help offset the extra moisture. It could take some experimentation to find the optimal additional amount of flour needed.
Hope that helps. 😀
-Adam