Is there a substitute for dashi?
Dashi (だし) is a class of stocks, and while katsuodashi (かつおだし) made with bonito flakes is the most common type, there are plenty of alternatives.

The most common purely vegetarian one in Japan is kombudashi (昆布だし, こんぶだし) made from kelp.  You can try to make your own, but well-stocked Japanese grocers will have powdered instant versions of this in stock.  Here's one from Ajinomoto:



Note the green packaging to differentiate it from the red/pink katsuo versions.  We use kombudashi often at home, and in miso soup etc the taste is not noticeably different from katsuodashi, although it does lack the strong "fishy" notes.