Dumplings... Hmmm... Maybe Bamboo Garden (near Seattle Center)? Or Teapot (Capitol Hill)?
Teapot on Capitol Hill is closed. Sadface. But for dumplings, I recommend Northwest Tofu on 19th and Jackson. They have lots and lots of vegan stuff...just ask, they are very friendly. I also recommend the salt and pepper tofu there, and the green onion pancakes.
Another dumpling option is Samurai Noodle. They have locations in Capitol Hill, U District, and International District. They have an awesome happy hour where you can get one appetizer (one of the vegan options is dumplings), a beer or sake, and a serving of edamame for $5.
In The Bowl is a yummy vegetarian noodle place in Capitol Hill and has dumplings. I can't vouch for the dumplings but everything else is yum.
And Bamboo Garden.