I've found nuts are basically a super food. No need for refrigeration or preservatives/processing to keep edible. I always have bags of shelled organic nuts on hand and eat handfuls on a daily basis. The only down side I've found is cost; nuts, especially organic ones, are more costly than filet mignon per lb at whole foods.
Note that the first non-meat source (other than fortified breakfast cereal) is baked beans and you'd have to eat at least a full can a day to get your RDI. Or I guess you could eat 2.2kg of yoghurt.
Walnuts have 3mg/100g (33% DV) [1]
Sunflower seeds 5mg/100g (53% DV) [2]
I'm currently holding a 340g bag of raw organic walnuts I opened this morning, and it's nearly empty just from snacking throughout the day. Also snacked on sunflower seeds, but not much.
Dinner was a large bowl of lentils, which have 3.5mg/100g (35%) [3]
Without even optimizing for it I'm over the RDI for Zinc without animal products, this is just what I happen to be stocked up on currently. So clearly it's not much of a challenge for a vegetarian to get sufficient Zinc.
[1] https://en.wikipedia.org/wiki/Walnut#Nutritional_value
edit: Ok, according to "Devirian, T.A. and Volpe, S.L., 2003. The physiological effects of dietary boron."
> Boron is known to influence a variety of metabolic actions. It interacts with calcium, vitamin D, and magnesium, which are all important in bone metabolism. Boron accumulates in bone in concentrations dependent on the amount of boron consumed. Boron has also been found to increase steroid hormone concentrations in postmenopausal women and to have antioxidant properties, which could make it beneficial in preventing atherosclerosis