Apart from some fragments all the pre 1901 Irish censuses have been destroyed, so that makes early Irish research quite challenging.
Drumintin is 263 acres in size. In the 1901 census there were 5 houses and a population of 20. It was all agricultural land in 1901. Looking at a satellite image it’s the same today. There’s a few new houses but I doubt there’s more than 10 homes. The Dawson farm in 1901 (plot 2 on Griffiths) still looks to be a working farm today. Up at the end of a long lane. Why not call up and see who lives there. There won’t be anything of great tourist interest in Dromintin, unless you particularly like hedges or fields of potatoes and silage.
There is a Richard Dawson memorial at the side of the R188. You might want to visit it. He was a local MP.
https://monaghantourism.com/listing/the-dawson-monument/
That’s close to Ematris Church of Ireland. You might want to visit that too and the graveyard.
You ask about earlier records. There aren’t so many, and some can be difficult to access. However the tithe applotment records are on-line:
http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
They are a list of folk with land (in 1830 in the case of Ematris). Compiled for tithe purposes (a controversial church tax) they list all the farmers in most townlands. There were 6 Dawson farms in Drumintin in 1830: George, Richard, Mary, Edward, Thomas & Fanny. The two ladies are likely widows. Richard is unlikely to be Richard the MP. Just someone of the same name and perhaps a distant relation of the MP.
You say your ancestors left in the 1850s during the famine. The big famine was 1845 - 1847/8, and by the 1850s things weren’t quite so bad. Whilst the general impact across Ireland was dreadful, all I would say is that farmers weren’t hit so severely as they normally had other crops to rely on (barley, oats, plus dairy and other products, and so on). They may have lost their potatoes but they weren’t left with nothing as farm labourers were who had no other crops but potatoes. So if your family were farmers they may have seen their income drop but at the same time they probably weren’t starving. It was Ireland’s huge army of labourers who only had small plots of land on which they only grew potatoes who really suffered, and died in such dreadful numbers.
If you are interested a contemporary description, I have attached a letter written by a farmer in Co Antrim in 1848 describing how he saw the famine. You’ll see that though he lost his potatoes (which even then he was able to recycle for starch) he kept going relying on his other crops (many of which rose in price due to demand). He wasn’t too badly off. There’s a myth that there was no food in Ireland during the famine. There was plenty of food (much of which Irish farmers exported). The problem was that the average labourer had no money with which to buy it. That’s why they starved. The Government failed to take proper action to supply food but that’s another story. But your family are unlikely to have been starving. There were other economic factors driving emigration during the 1800s. A huge population explosion, a lack of employment (Ireland has no natural resources eg oil, minerals, coal etc) and so the industrial revolution just passed it by). The population had gone up from 3 million in 1741 to 8 million by 1841. There just weren’t jobs or land for all those folk. People had been pouring out of Ireland all through the 1800s. All the famine did was speed it up a bit.