I go out to Oz each year to see my son and his family via Singapore and the baggage gets loaded at LHR and comes off at Brisbane. Mind you, that's with SIA both legs. Emirates do the same. I would imagine any connecting flight with the same airline would follow the same procedure although that's just a guess on my part. There probably is a left luggage at Changi although I've never used it, they have everything else there. Best airport in the world IMO.