Thank you for your post to the message board. I am one of the members of the Tulla Reaching Out Heritage committee and I will be happy to assist you.
I do see the reference to Catherine Dodd born to William Dodd and Anne Sullivan both from Tulla. It would appear that both William and Anne lived in the town of Tulla. Martin Dodd was the noted witness to their wedding on 8 January 1832. I also see that Martin Dodd got married on 31 January 1832. This may be a sibling to William Dodd. John Sullivan was the second witness to this wedding, and he may have been Anne's father.
The Dodd family were not listed in Griffith's Valuation in 1855, but a John Sullivan was listed. I note that he was listed at Entry No. 25 & 26 and this area is just below the Fairgreen area. It is privately owned houses today, although I would have to look attes to see which house it might have been.
The Sullivan family had an ancestor who was in the British army. https://irelandxo.com/ireland-xo/history-and-genealogy/ancestor-database/martin-sullivan
There were Sullivan families in tulla village in the 1901 Census. One of these families ran a small boarding house on the Fairgreen in Tulla. If you like, I can make enquiries for you.
Let me know.