A new colony is called a mycelial mat. Since the organisms are ubiquitious is appears that the spots are contagious. In fact if the conditions are right and a nutrient source is available, growth would take place no matter how many dolls are in a given location. Given that, I would not say that the microbial attack is the result of a contagious phemomenon. The bad news is that if the dots appear in a painted area the paint will be removed.
Microbial growth is a surface phenomenon.
A doll that is supporting fungal growth can be cleaned and restored. If the doll is again subjected to high humidity new growth will begin again. If a doll that has fungal spots is taken into a room with other dolls the other dolls will not automatically begin to grow fungi. With that in mind there is no contagion. There are millions of fungal spores in the air we breathe.