There's no burial at Belfast City Cemetery, Dundonald Cemetery or Roselawn that matches that name and quarter-
http://www.belfastcity.gov.uk/community/burialrecords/burialrecords.aspxAlso no Will Extract on PRONI's site.
You might have to buy the certificate to get more details but it will not list a place of burial. See here for what information is given on Irish death certificates- and a Roscommon research certificate would be a better option if you do decide to go down that route-
http://www.rootschat.com/forum/index.php?topic=433043.0The death index shows that Thomas Mills as age 34 (born c1883).
https://familysearch.org/pal:/MM9.1.1/FR24-P27Burials were not always in churchyards and there are numerous other possibilities in and around Belfast. Another possibility is that he was buried in a family plot whereever his family came from which may not have been near Belfast. Also, there's a good possibility that there's no headstone or other record.
Since you are in canada and searching the Belfast papers isn't an otpion- have you tried Quebec papers to see if a death notice has posted? Does his service record not have a mention of when he died?
Have you checked CWGC site to see if he's listed? (if so will give place of burial).
You've actually posted this in ANTRIM RESOURCES & OFFERS (which is not for queries)- just click on 'report to moderator' and ask for it to be moved to ANTRIM board.