The May 1844 baptism shows father as Francis Emmerson-
https://registers.nli.ie/registers/vtls000633057#page/22/mode/1up
A Catherine Duffy appears as sponsor for all three baptisms.
Are you sure Mary's sponsor was Catherine Duffy? The nearest I could get to Sponsor 1 was Lally.
This register may be a transcription of original register(s). A note to one baptism is "Torn away sponsors' names".
I looked at other adult baptisms in those years for comparison but I'm no wiser. See:
26th April 1844 John Devanney, parent Jane Cadman, Sponsor Abraham Doherty. (Unless Abraham belongs to previous baptism.
)
11th June Patrick & William Canning and James Canning who may have been their father or another being baptised. No sponsors.
Same day John McLaughlin, no sponsor. His name is in parent column. At a cursory glance it looks as if James Canning and John McLaughlin were the parents of Patrick & William Canning.
(There are some 1843 pages in with 1844 so I'm not sure if this is 1843 or 1844.)
See also next double page which is 1843:
8th July Ann McPeak
21st July Eliza Jane Kerr
23rd July Margaret Mulhearn
11th Nov. 1845 Eleanor Boyle
1846:
23rd March Matthew Henderson
14th July Mary Kelly & Sarah Moss, Adults, converts
10th Aug. Elizabeth & Sophia Rolles, adult Protestants
16th Aug. Thomas Miller, adult convert
20th Aug. Jane Doherty
5th Dec. Ann Jane Given
Some of the names are in the parent column. None except John Devenny and possibly William & Patrick Canning have a parent or sponsor named.
If all those baptisms 1843-1846 were by the same priest and if he was consistent when he wrote them up, it's possible that Mary and Wiliam Emmerson and John Devanny were older children or adolescents. That's 2 "ifs". The order of sacraments for Catholics at that time was Baptism, Confirmation, First Confession (?), First Holy Communion. Typical time for the last 3 would have been sometime between later childhood (maybe 10+) to late adolescence or early adulthood. I'm thinking that Mary and William hadn't reached the usual age for Confirmation & First Communion.
I was considered (by my own family) old enough to be a godparent at age 10.
My supposition for possible ages of Mary and William at baptism don't match info re their ages on 1861 census.
Ancestors of mine in England had their eldest 3 children baptised in C. of E. as babies then got them "done" again at a Catholic church, aged 1, 3 and 5. Baptism register includes date of birth of each child.