Looking for children of Thomas Quinn and Jane Hunter

Tradition was to marry in the bride’s church, after which she’d normally attend her husband’s. Thomas’s townland was Grange in the parish of Bright. Unfortunately Bright’s early Church of Ireland records were destroyed in the 1922 fire in Dublin (as were the records for Dunsfort) so sadly if that’s where Joseph was baptised you won’t find any records. However labourers moved around a lot to follow the available work so it's possible the family were in some other nearby parish by 1849. You could search those records.

The general answer to your question of where Church of Ireland baptism records are kept for Co. Down is PRONI (the public record office) in Belfast. They have most of the surviving records on microfilm there.  Some Church of Ireland records are also on-line on various pay to view sites but the majority are not. There is a project going on at present to put all the Church of Ireland records on-line on the irishgenealogy site but it still has several years to go (and has probably been halted at present due to Covid).

I searched for statutory births 1864 – 1877 to see if the couple had any children after statutory registration started but did not find any. 

Thanks