I grow a lot of herbs all year round, due to our climate here..............We also grow a lot of onion family. the dogs are just not interested in those. We grow a very large Tansy, which is not edible, but the dogs often lie in that and flatten it. It works well on keeping fleas away. And my dogs never have fleas. They also like the crash through the lavender and it does the same. They smell nice when they do that. The geranium family is also insect repellant. The main parsley, rosemary,sage, marjoram, oregano and coriander are OK for animals. Some like wormwood, which is not an eating herb anyway are poisonous, but our dogs have no interest in them. I have been growing vegies and herbs for as long as I have had newfs and have never had a problem. The only plant that you have to be really extremely careful (every part is bad) with that i did have is an oleander (not a herb).............There are many poisonous plants and most have a milky sap. But most plants edible to us are OK. Actually rhubarb is another that can be bad if eaten uncooked. But again they show no interest. Tessa loves Comfrey and often eats it (small amount) and she loves Parsley, Annabelle just looks and goes"what are you doing?".Chamomile is another she like to eat. Keep the green potatoes away from them too, but they are also bad for us.
If you are more specific, I have lots of herb books and can always check. Ofcourse the great google.........Herb+dog.........might do it too
Have fun, it is very satisfying to grow your own without chemicals
Ronnie
