DavidW have you actually gone through all of the 6th Division war diaries (there are also war diaries for I Australian Corps) at the AWM website. Have you checked: Second World War Diaries - AWM52, Item 1/5/12 | Australian War Memorial
Also, all of the official histories are on-line as well.
Here is my summary history for 2/1st Anti-Tank Regiment:
2/1st Anti-Tank Regiment, RAA
October 1939 in Queensland (except for one battery from Tasmania)
1st, 2nd, 3rd, 4th Anti-Tank Batteries
The regiment was originally raised as 2/5th Field Regiment but was shortly called 2/1st Anti-Tank Regiment. It formed part of 6th Australian Infantry Division from its formation until the end of the war. It went to England with 18th Australian Infantry Brigade leaving Sydney on 4 May 1940 and arriving at Glasgow on 17 June 1940. It was broken up in England as two independent batteries but reformed in September 1940. It left England on 15 November 1940 and arrived in Alexandria on 31 December 1940. It served under the division during the early campaigns against Bardia and Tobruk until February 1941, when the division was withdrawn to Alexandria. The regiment then went with the division to Crete, arriving on 3 April 1941. It was evacuated at the end of April 1941 and returned with the 16th Australian Infantry Brigade for Egypt and Palestine. One Troop served under 4th Cavalry Brigade in Syria from June to July 1941. It was then attached to 6th British Infantry Division in Syria from July to October 1941.
The regiment left Syria in early March 1942 for Australia. In April 1942, 2nd Battery served under command of 11th Infantry Brigade at Townsville. One 6-pounder of the regiment was used in December 1942 on the Sanananda track in New Guinea. The regiment remained in Australia until October 1944, when it served under the division in New Guinea at Wewak.
There was no 2/1st Light AA Regiment until August 1941. See my summary for 2/1st Heavy AA Regiment below:
2/1st Heavy Anti-Aircraft Regiment, RAA
1 May 1940 in New South Wales
1st, 2nd, 3rd Batteries
The regiment was formed as part of corps troops with 1st Battery formed in New South Wales and 2nd and 3rd Batteries in Victoria. On 29 June 1940, half of 2nd Battery was sent to Darwin. It arrived on 1 July and moved to Larreykah Barracks with the 2nd Section at Darwin and 3rd Section at Parap Camp. It remained there until December 1940, when it was replaced by 14th AA Battery and was recalled to Sydney. It left Sydney for the Middle East in June 1941 and arrived on 25 July 1941.
In August 1941, it was converted to a Light AA Regiment and served under 1st Australian AA Brigade in Palestine. It then served under 7th Australian Infantry Division during the invasion of Syria. It returned to Australia with 7th Australian Infantry Division and corps troops in March 1942. It was sent to the Darwin area after the 19 February 1942 Japanese air raid. It had the responsibility of the AA defence of all airfields in the Northern Territory area. The 3rd Battery was sent to Port Moresby to form part of its AA defence on 11 April 1942. The regiment reformed as 2/1st Composite AA Regiment in July 1943 and became part of I Australian Corps Troops. It was located at Finschhafen in October and November 1943. It returned to Queensland in early 1944 and remained as corps troops until the for the rest of the war. It served under I Australian Corps in the Balikipan, Borneo landings from 1 July to 15 August 1945.
3rd Battery, which left the regiment when it became a Composite AA Regiment, landed with 7th Australian Infantry Division as an airborne unit at Lae-Nadzab in early September 1943. It served there until