Dogs went to war with us in WW1 and WW2 in both cases protection was provided for our furry friends with provision of gas masks. Bit extreme for just blocking out dust but I would imagine that it will be easier to source NBC gear or BA sets for dogs than it will be to source dust masks. Probably expensive though.

While discussing this though a dog will need to be acclimatised to wearing a mask. Dont expect the dog to understand that that thing needs to be on its face just because its dusty. Some dogs will happily "wear" their owners spectacles or hats but some will not.