It's the date for Richard that's more important... problem is that he was born before the start of registration of births, so you have to check for a baptism instead, obviously doing that properly depends on knowing the religion of this family and exactly where in 'Dublin' they lived, i.e. which parish, town or part of the county, i.e. if it was somewhere outside the city. Church records for most parishes in Dublin city area are on the free IrishGenealogy website, mostly Catholic and Church of Ireland - however there are several Church of Ireland parish registers damaged so not available
If that Mary is his mother it looks like she remarried, otherwise why is she shown as 'Curran', so maybe a search for a second marriage for her in England and Ireland might be one line of investigation to follow up on, I would also suggest checking up on that marriage for Richard and Sarah, a) to confirm his father's name and occupation and b) to check witnesses.. it may also be worth checking for a death for Laurence/Lawrence (if that's confirmed as his name) in England
edited - that Mary Curran is more likely his mother in law not mother as the census form suggests