Can't really help about eating vegetarian. As the south Tyrol valleys belong mainly to Austrian/German culture, vegetarian cooking may not be their main field. I would even consider renting an apartment and cooking on my own - first class produces up there. Dobbiaco has a sort of dairy boutique to die for (but I do not know if dairy produces are good for you). Wines from the south tyrol region - Traminer, Sylvaner, Lagrein, Pinot - are top quality.
From Dobbiaco you could drive to Cortina - even the extremely scenic Falzarego pass is not impossibily distant - to Tre Cime di Lavaredo, to Braies lake. From Sesto (twenty minutes by car from Dobbiaco) you can walk along the Val Fiscalina on the back of Tre Cime, and I remember doing some hikes from Monte Croce Comelico.
All the area was a fighting theater during 1st world war. In the area of Monte Piana there you can still see the trenches where the war was fought (every now and then you can even find a boot sole or bullet shells or shrapnel splinters. The area on the higher station of Falzarego cable car was also a fighting area, there Italian soldiers built an helicoidal tunnel in a mountain and had the top of it exploded. The tunnel can be walked at present but a little dangerous if you do not have appropriate equipment including lights and heavy boots. Even if you do not walk the tunnel the area has a lunar landscape you would not believe. The cable car closes around mid-october (I read on the web their last day is Oct. 23rd).
Brunico and Bressanone are possible city visit within an hour driving.
As for having lunch around the way, my favorite stop is in Isera near Rovereto - stopped there three days ago - but it is not vegetarian and you would probably get there around 3pm - too late for lunch.