Many fonts on Typekit support Dutch. You can browse fonts that support Dutch by selecting "Dutch" from the list of supported languages in the sidebar under browse fonts.
After you have added a font to your kit, choose the "All Characters" option or create a custom language subset which includes Dutch to add the language to your kit. Republish your kit, and the Dutch characters will be available to your website within a few minutes.
The Language Support & Subsetting help page has more information on the character set options.
All fonts that support Dutch include the following letter characters, at minimum: