In my freezer I keep a bag of all vegetable trimmings. When it is time to make stock, I pull out that bag and incorporate those vegetables into the stock. Usually I end up adding all the ingredients here as well as those vegetables, so you should try to think of this recipe as the base for experimentation. It is good on its own, but can be added to.
As I’ve made different batches of stock, I’ve learned which vegetables I like in stock and which ones I don’t. The mushrooms are a particularly lovely addition. They add a certain depth to the flavor. I don’t particularly like beet in my stock, but milder root vegetables like turnip or parsnip make a great addition. Leeks, green onions, asparagus stems, greens stems, tomato, etc. etc. etc. You get the idea.
I never add salt to my stocks, since it allows for greater control of the overall salt content when you’re using it as an ingredient in other dishes. Feel free to add it, though!
NB: Dogs should not eat any onion or garlic. Seriously. You can, however, compost those things.