The 14th Indian Infantry Division was raised on June 1, 1941, at Quetta in Baluchistan and placed under Major General Wilfrid Lewis Lloyd.
This Division was not due in Burma until April (by which time there was nowhere for it to land after Rangoon had fallen). If Rangoon had not fallen at this time, what would have been the OOB of the 14th Indian Infantry Division?
From a table in one of the volumes of Nafziger's THE BRITISH ARMIES IN WORLD WAR TWO AN ORGANISATIONAL HISTORY, by Hughes et al (specifically Volume Eight):
1941:
14th Indian Infantry Division
23rd Indian Infantry Brigade
36th Indian Infantry Brigade
37th Indian Infantry Brigade
1942:
14th Indian Infantry Division
23rd Indian Infantry Brigade
36th Indian Infantry Brigade
47th Indian Infantry Brigade (from 19th Indian Infantry Division)
49th Indian Infantry Brigade (from 19th Indian Infantry Division,
then to 23rd Indian Infantry Division)
55th Indian Infantry Brigade (from 7th Indian Infantry Division)
1943:
14th Indian Infantry Division
23rd Indian Infantry Brigade (then to 5th Indian Infantry Division)
47th Indian Infantry Brigade
55th Indian Infantry Brigade
Your "23rd Indian Infantry Brigade" sounds more like the British 23rd Infantry Brigade (of the 70th Infantry Division):
1 Essex Regiment is assigned to British 23 Inf Brig from 17 Oct 1941 to 17 Jun 1945; 23 Inf Brig doesn't arrive in India (from Egypt) until 8 March 1942
2 Duke of Wellington's Regiment is in India as of 3 Sep 1939, it is not "mobilized" until 1 Feb 1942 and it then goes to Burma and arrives 14 Feb 1942. And thereafter is assigned to 46 Indian Inf Brig - 17 Indian Inf Division
4 Border Regiment is assigned to British 23 Inf Brig from 29 May 1941 to 28 Oct 1944; and, again, is with the Brigade in Egypt until the Brigade goes to India
It would be unusual for three British infantry battalions to be assigned to an Indian Infantry Brigade, unless that Brigade was designated (or re-designated) as British Infantry Brigade
And 14th Indian Infantry Division would have more artillery, at least another Field or Mountain Regiment and an Anti-tank Regiment (or even a battery)
If this brigade remained with the 14th Indian Infantry Division it would indeed be probably composed of three Gurkha battalions
3/3 Queen Alexandra's Gurkha Rifles (formed 1 Oct 1940), assigned to 37 Indian Inf Brig, late 1941 and remained with brigade for the rest of the war
3/5 Royal Gurkha Rifles (formed 1 Oct 1940), assigned to 37 Indian Inf Brig, late 1941 and remained with brigade for the rest of the war
3/10 Gurkha Rifles (formed 1 Oct 1940), assigned to 37 Indian Inf Brig but not until late 1942 in Burma. Before that battalion was stationed at Quetta and assigned to Quetta Brigade. It remained with 37 Indian Inf Brig for the rest of the war
As noted 37 Indian Inf Brig was originally assigned to 14 Indian Inf Division but transferred to 23 Indian Inf Division in 1942
"36th Indian Infantry Brigade
5th Bn 16th Punjab Regiment
8th Bn 13th Frontier Force Rifles
1st Bn 8th Gurkha Rifles"
Try this slightly different version:
7/5th Mahratta Light Infantry (formed 1 Aug 1940), assigned to 36 Indian Inf Brigade late 1941 and detached to 268th Indian Armored Brigade late 1942 (later converted to 51st Regiment Indian Armored Corps and then to 8th Mahratta Anti-Tank Regiment)
8/13th Frontier Force Rifles (formed 7 Aug 1940), assigned to 36 Indian Inf Brigade late 1941, and remained with brigade to the end of the war (except assignment to the Lushai Brig in late 1944)
5/16th Punjab Regiment (formed 7 Aug 1940), assigned to 36 Indian Inf Brigade late 1941, and remained with brigade until late 1944
then
1 North Staffordshire Regiment assigned to 36 Indian Inf Brigade 1 Oct 1942 to 11 Sep 1943
1/8th Gurkha Rifles is not assigned to 36 Indian Inf Brigade until early 1944, it is stationed at Thal 1940 to 1942, then assigned successively to 55, 106 and 116 Indian Inf Brigades
4/5th Mahratta Light Infantry (formed 15 Oct 1941) assigned to 23 Indian Inf Brig late 1941, then detached to 49 Indian Inf Brigade late 1942
8/10th Baluch Regiment (formed 1 Feb 1941) assigned to 23 Indian Inf Brig late 1941, then detached to 123 Indian Inf Brigade late 1942
1/15th Punjab Regiment (regular) assigned to 23 Indian Inf Brig late 1941, then detached to 123 Indian Inf Brigade late 1942
I am wondering if 23 Indian Inf Brig was renumbered as 123 Indian Inf Brig when it was assigned to 5 Indian Inf Div in late 1942, to avoid confusion with the British 23 Infantry Brig which had arrived by then in India?