Would it be okay to use Quick Oats or Old Fashioned Oats?

Of course. It won't have the same texture or toothiness as steel cut but will still be tasty and is just as good for you. I would use half milk and half water (or just water), and cook according to package directions. Once the oats have cooked, turn off the heat, and let the oats sit covered on the stove for five or so minutes to let the oats soak up any excess liquid, then melt in the Parmesan or Pecorino or whatever cheese you're using, and garnish to your heart's delight.
P.S. If you're using regular oats out of respect for time, there are some brands now carrying quick cooking steel cut oats, like Bob's Red Mill and Mc Canns, which I highly recommend trying, but use what ever you got, even quinoa, or bulgar or just about any grain would still work with this recipe with a little tweaking of the cooking time/liquid ratio.
I hope you enjoy it!!