There are no Qualtrough MI's recorded by Oliver in 1868 - see www.manxnotebook.com/manxsoc/msvol14/mem18.htm - unfortuneately Feltham missed out on Braddan in 1798 and this was an attempt by Oliver to record those stones he would have seen - when I did a brief comparison with the Braddan MI's published in 1980's it seems as if several of these had already gone (probably damage during the open air services until they were moved to an adjacent field) - what I didn't do (which was remiss) was to see how comprehensive Oliver was - he didn't include many later stones so he was obviously selective - maybe he missed yours !.
AFAIK this and St Georges (too late for your period) were the only burial grounds for South Douglas - Onchan handled North Douglas and it seemed buried proportionaly more 'strangers'.