I'm not in Missouri, but I do have dogs. :) A couple thoughts - I think the most obvious is fencing off your garden area, but maybe that isn't practical for you? If your dog doesn't like the herbs, I'd also try surrounding your beds completely with the herbs she doesn't like, hopefully detering her from crossing into the veggie area, or interspersing the veggies with the herbs so she doesn't notice them as easily. Otherwise, I think the container garden idea sounds great - you might also want to try those topsy-turvey type tomato planters - just remember that it'll require more water than an in-ground bed.
Best of luck - hope you find a solution that works!