What if: Force Z (HMS Prince of Wales and HMS Repulse) and a carrier named HMS Indomitable

  Doubt it as there wasn't the facilities to support capital ships there.  Ceylon didn't have the same resources as Singapore but a lot more than Australia. 

  Its likely that Somerville might well try and use two fast and reasonably well armed ships in such an operation, although that would mean them being separated from the older and slower R class ships that formed the bulk of the Easter Fleet OTL.  Or possibly he keeps them with the carriers to boost the AA defence of the latter.

  Depends on the circumstances.  The Japanese deployed a powerful force in the Indian Ocean raid but whether they catch the British fleet and the fact it has a markedly more powerful air defence, if they did so the force might survive, although quite possibly to be with heavy losses.

  Agreed.  Still could well be lost later in the war but once Midway occurs, if not butterflied, and with the allied air strength building up they could provide a heavy firepower strength that the forces lacked OTL.

  In Dec 41 I think they were the only such ships east of Suez.  Also Nov/Dec 41 was a bad period for the RN.  As well as the historical loss of Force Z we lost the BB Barham and CV Ark Royal in the Med while the refitted BBs Queen Elizebeth and Valient were struck by human torpedo attacks in Alexandria harbour and badly damaged.  For a while Britain didn't have a single capital ship in the Med.  The RN scrapped together a fleet to operate in the Indian Ocean but while this had two modern CVs the capital ships consisted of the old but modernised Warspite and the surviving members of the R class, which were largely unmodified from their completion in WWI.  [Wiki said all 4 of them were sent to the Indian Ocean in 1942 but I'm not sure all of them were.  Know that later Royal Sovereign was sent to Russia as a loan until they got one of the Italian ships after the latter's surrender.  It was returned in very bad condition and the Soviets never got an Italian ship.]

  Basically this was the time the worst time of the war for the RN.  As well as being at maximum stretch in the Atlantic against the U boats the continued loss/damage of ships and commitments in all oceans meant massive overstretch, at least until the US could start taking the strain, initially in the Pacific and later the Atlantic.

  Presuming the other OTL losses occur I could see the two ships, presuming they end up largely undamaged at Columbo, being joined by the two CVs, to give a modern fast force.  Might see Warspite join them as althrough slower and older it has been modernised in the 1930's.  Suspect given the lack of ships in the Med it would probably stay there.

  If we had such a modern fast force I couldn't see much point in sending the old R class units there.  They might continuing being heavy convoy escorts or some laid up to release manpower for newer, more important units.

  The two that were present in early 42 during the period of the Japanese raids into the Indian Ocean were HMS Indomitable and Formidable.  Think after Midway removed the immediate threat they may have been transferred elsewhere to 'hotter' regions of the war.  Formidable, according to its Wiki entry stayed in the Indian Ocean to support the landings in Madagascar in mid 42 then returned to Europe to support the Torch landings.  Checking on Indomitable it also had a similar stay in the Eastern fleet before heading home after Madagascar.