Ancestry.co.uk currently have WWI medal cards free to view until the end of the year (if you create an account with them) - it saves you paying £3.30 with the national archives.
His medal card can be found on there if you search for Donat White.
It doesn't say a great deal though to be honest. He was awarded the Victory, British and 1915 Star medals. He first landed in France on 17th December 1915 which is why he qualified for the 1915 Star which is rarer than some of the other WWI medals.
More interestingly and useful to you though, is I have found he was also awarded the Silver Badge in 1917. This was given to men who were wounded in action.
It states the following:
First name(s) Donat
Last name White
Service number 8/1970
Rank Private
Badge number 140349
Enlistment date 03-May-1915
Discharge date 04-Jul-1916
Unit from which discharged The Royal Munster Fusiliers
Cause of discharge Wounds, 392 (xvi) King's Regulation
Whether served overseas Yes
Badge date of issue 07-Mar-1917
(An explaination for the cause of his discharge can be found www.forrestdale.pwp.blueyonder.co.uk/KingsRegs1912/Para392Introduction.html)
I haven't found a service record for him (yet). Its possible it was destroyed in WWII so no longer exists (many WWI records were destroyed). If you have a year of birth or a place of birth, that would be very helpful, because if his record exists, I think it will be listed under D White rather than Donat, which is a bit of a nightmare to search through one by one.
I strongly suspect he was part of the 8th (Service) Battalion as the date on his medal card for landing in Europe is only a day out as the date official given for the battalion landing there (this isn't uncommon). They are listed as 18 December 1915 : landed at Le Havre.
The battalion diary is available to buy at the National Archives here: discovery.nationalarchives.gov.uk/SearchUI/Details?uri=C7352859 for £3.30. These diaries rarely mention the names of individual soliders but they do give a fairly detailed report of the day to day actions of the battalion - giving descriptions of what the battle orders were and descriptions of the day. They vary in detail - some are more in depth that others, and is entirely down to the officer who was making the records. They can be very insightful about the conditions though. It certainly would tell you what battles he was involved in.
The 8th Battalion received a reinforcement of 200 men on 30 May 1916 and Donat was discharged from service on the 4 July 1916. I would strongly suspect that Donat was actually injured before this reinforcement... Men usually took a while to be officially discharged (being repatriated back to England commonly took upwards of a month). I think he would have served in the Loos Salient area.
1914-1918.invisionzone.com is a very good source of information and they have a good forum which is both worth search or posting on.
I may have done a little bit of similar research with my family 