How does the girl in Vermeer's painting represent the new merchant class springing up in Denmark?

The girl represents a new era of rising wealth for the merchants by reflecting a new art scene that had succeeded in breaking away from the Spanish Catholic rule.

Explanation:

I am going to assume this is Vermeer's painting of The Girl with the Pearl Earring.

This was painted in 1665 around the time the Dutch had succeeded at breaking off from the Spanish Catholic rule. This suddenly allowed economic development as well as a rising art scene that was now free to deviate from religious subjects that had previously been strictly enforced on the people.

Around this time the rising wealth of merchants made them desire artwork and personal portraits. To have a portrait painted was a symbol of wealth.

Vermeer himself painted many portraits of merchant's daughters over this time, as it reflected the new "domestic bliss" (as some would say) of the newfound peace and artistry of this era.

You could even say that this portrait represented a new era and economic growth for merchants (and many others). Reflecting the beauty of everyday life, wealthy people who wanted to flaunt how well they were doing in this time of growth, and the fascination of capturing everyday chores and expressions instead of being conformed to stiff, religiously inclined works.

I hope this helped at least a little bit :)