The key piece of information here is the mention of Arderry on Thomas's baptismal record. From the way it is written it could infer that either of his parents were from Arderry - as the Creers of Ballawillyn owned Arderry for a time - but they only bought their southern piece of Arderry from Thomas Quine of Arderry in 1760 ie after this birth - so we must therefore conclude that Thomas Quine, husband of Kath Creer was of Arderry and not Kath Creer. However this then causes some confusion as I understand, from the work Nigel Crowe has done on the Quines of Arderry, that the Thomas Quine who sold Arderry in 1761 was married to Margaret Creer. Margaret was the daughter of William Creer and Catherine Taggart of Ballamodda - she died in 1777 and her will makes no mention of a son Thomas Quine as Sue points out above. Margaret Creer married Thomas Quine of Arderry in Oct 1744 which is consistent however with a son baptised in 1750.
The confusion is compounded by the absence of any marriage record being found for a Thomas Quine and a Kath Creer - nor did the Creers of adjoining Ballawillyn have a daughter Kath as far as I can tell. According to the IGI there was a Kath Creer born in an neighbouring Creer family in Baldwin, at the Larghey/Algare, in 1725 to Patrick Creer and Margaret Callow, but there is no record of her marrying a Quine - not mentioned in her father's will for example.
So based on the hard evidence that the family was from Arderry I believe that Thomas Quine baptised in 1750 was a son of Thomas Quine of Arderry and Margaret Creer (the Kath Creer being a transcription error!) and he cannot have survived long as there is no other record of him later on.
Hope this helps