I suggest you spend some time on the Long Long Trail website
http://www.1914-1918.netThis splendid site is packed with information about the army in the Great War - and will tell you that the Royal Dublin Fusiliers and the Labour Corps were two different elements of the army. Neither are very specific as both were elements of the army that put multiple units into the field in multiple theatres of war. To understand more about your great-grandfather's involvement you will need to find out more details - eg Which battalion of the RDF was he with? Which Labour Corps company?
The Long Long Trail has a section on researching soldiers - a good starting point.
If when you say 'at the Somme' you are referring to the Battle of the Somme in 1916 then the Labour Corps was not involved at all - because it wasn't formed until January 1917 over a month after the end of the battle. Of course there was plenty more fighting in the Somme area of the front - in which elements of the Labour Corps would have been involved, especially in the chaos of the German Spring Offensive in 1918.