Wordorigins.org

This is one of several derisive terms referring to the Dutch. Dutch treat is an Americanism referring to the supposed Dutch trait of being miserly. It dates to at least 1887. From the August issue of Lippencott’s Magazine of that year:

"You’ll come along too, won’t you?" Lancelot demanded of Ormizon. "Dutch treat vous savez."

The adverbial form go Dutch dates to 1914.

(Source: Oxford English Dictionary, 2nd Edition; Historical Dictionary of American Slang)