Where do you live? I don't know of any US company that would make this. Your best bet is probably to get vegan yogurt and strain it. Get some cheesecloth and a fine mesh strainer and set it over a bowl in the refrigerator. The first time you'll have to watch it carefully to see how long it needs to get to the thickness you like. It won't be exactly like quark, but it's probably the closest you can come.
The only recipe I could find that I could read was an Italian one that says the same, but adds salt and and a little lemon or lime juice to the yogurt before straining. The other recipes are all in German, and the only thing I know how to say in German is "I am a large train station." Not very helpful.
Vegan cream cheese would be the next best substitute, probably. Again, if it's for a recipe, add some lemon juice or vinegar to give it the right sharpness.
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