There is no immigration or customs to deal with in Domestic travel.
For ID, provincial health card should be fine. See here: https://www.publicsafety.gc.ca/cnt/ntnl-scrt/cntr-trrrsm/pssngr-prtct/dcmnts-eng.aspx
Usually you need 1 piece or ID if it has your picture, name, date of birth and gender... or 2 pieces of ID if there is no picture on it.