I don't believe in using peat moss for the aquarium, with the exception of for certain types of fish who need it to spawn. It doesn't lower pH or softness significantly, and there are better alternatives.
Plus, harvesting peat is not environmentally friendly. Peat moss is derived from sphagnum moss, which is the main component of bogs, one of the most endangered wetlands out there. Its very, very slow growing, and it takes a long time for live sphagnum to decompose into peat soil. In order to get to the peat, live sphagnum moss is torn away and discarded (or used for other purposes), and an entire bog basically dug up and destroyed.
You can get tannins and lower your pH using oak leaves, as well as driftwood, or even those ridiculous Indian almond leaves.