If it's mild COPD, it shouldn't be grounds for withholding your Dad from a flight at all, but as VS-LHRSCA said, they'll want to cover themselves at check-in.
Get a travel certificate from your Doc prior to travel, (should be dated within 2 weeks of travel) whether you decide to order the therapeutic O2 or not. This will make everything easier and hopefully smoothe the way. If you do elect to order the O2 give the airline plenty of notice. I'm not sure about SIA, but some require a couple of weeks.
Make sure your Dad takes his prescription for his medication (albuterol I'm guessing), and a goodly store for his trip. It's readily available in AUS, but it doesn't hurt to be prepared.
Hope your Dad has a safe trip.