The British-English adjective demob happy (when used predicatively), demob-happy (when used attributively), means:
feeling elated
– in anticipation of demobilisation from the armed forces,
– hence, in anticipation of the end of a job, assignment, etc.,
– and, in extended use, in anticipation of the end of any onerous or unpleasant period.

Note: The adjective happy has been used as the second element in other compound adjectives, particularly common during and following the Second World War, relating to mental instability associated with the first element—as in trigger-happy.

The earliest instance of demob happy that I have found is from a letter published in the Liverpool Echo (Liverpool, Lancashire) of Wednesday 5^th December 1945:

“DEMOB HAPPY”—BUT

It is a blow to return to B.A.O.R.¹ and see the difference in the lot of English people compared with the Belgians. I recalled on my last leave going to the grocers’ and supreme optimist that I am, I took a paper bag. When I had been given what I was entitled to, I realised that I could have put the whole darned lot in with my field dressing pocket!
The Dutchman is broke because the main source of his wealth (the Indies) was occupied by the Jap. The French, to a certain extent, are in the same boat and one can go through the various countries, and find a similar state of affairs. Mainly they are broke because their own cheap source of raw material was involved in the war and occupied by one of the Axis partners. But not so the Belgians with their Congo (which was in Allied hands) and materials taken were paid for and, I presume, worked by the Allies. The Belgians seemingly have plenty of francs, dollars, pounds, guilders. &c., for exchange abroad. At the moment I’m “demob happy,” but what is there in England? Strikes, sparse rations, clothes few, and maybe not a house. Still there is a wife, kids and friends.—J. J. S.

¹ B.A.O.R.: British Army of the Rhine

The second-earliest instance that I have found is from a letter published in the Nottingham Evening Post (Nottingham, Nottinghamshire) of Friday 25^th March 1949:

HIGH-RANKING VISITOR

Here is a brief account of some of the preparations made in our training unit a few days before the visit of a high-ranking Army officer. Immediately things began to happen. All damaged barrack-room chairs were recalled and new ones issued. All deficiencies in electric light bulbs were made up. New brushes were issued to barrack rooms. The radiators were hot all night, and there was hot water in the washrooms. Pictures were put up in the cookhouse, and the food improved miraculously On the day of the visit the meals were fit to grace a banquet table. All N.C.O.s² not on duty in the evening were ordered to remain with their squads “doing something intelligent” until lights out. This just goes to show what happens when a high-ranking officer visits a unit expecting to see a “normal” day’s training. No wonder he is satisfied.
DEMOB HAPPY.

² N.C.O: non-commissioned officer