Cody (or Coady) and Barnwell Surnames - 1840's to 1850's in Wexford

[Wexflyer]

And it's worded "minor daughter of"... Edward and Mary , etc.

Well, anyone under 21 was a minor.

As for Cody versus Codee - you need to understand that chances are probably around 99% that this is not their own spelling, but the spelling guessed at or used by the priest or official, who in Quebec might not be a native English speaker himself.  Standard Irish spelling would probably be Cody, with Coady as a less common variant. Certainly not Codee. For example, in Griffith's Valuation there are:
Cody -  1,234
Coady - 34
Codee - 0

[TTILL]

Excellent - you are a guru and I'm grateful for the insight/information.  Was there a reason you felt they were not from Wexford?  I truly wish to visit Ireland/Northern Ireland again - with the hopes of exploring the region.  I'm confident on my Lynch trail and the family being at the Workhouse in County Tyrone prior to sailing to Quebec.  I'd very much like to track to the family in Wexford.  Thank you. 

[Wexflyer]

Excellent - you are a guru and I'm grateful for the insight/information.  Was there a reason you felt they were not from Wexford?  I truly wish to visit Ireland/Northern Ireland again - with the hopes of exploring the region.  I'm confident on my Lynch trail and the family being at the Workhouse in County Tyrone prior to sailing to Quebec.  I'd very much like to track to the family in Wexford.  Thank you.

Just to be clear, it was not that I did not think they were from Wexford, rather I just wanted to understand your basis for thinking so.
If you go to
https://askaboutireland.ie/griffith-valuation/
And first search for Cody in Co. Wexford, and then Coady, you will find 83 Cody families and 2 Coady. That was in 1853 though, after your family left.