I'm sure an identical question came up a few months ago.
The Ark Royal won't be going to the Indian Ocean in 1942 as she was needed in the Med. With the Ark Royal still around then the USS Wasp won't be required so she could serve in the Pacific earlier than OTL.
Ark Royal would be used in Operation Pedestal instead of the old and slow Eagle and would stick around the Med until 1943 supporting Torch, Siciliy and Salerno and then go home for a long refit. We would see her in the Indian Ocean in 1944 and maybe the BPF but not sure.
If Ark Royal is still around in the Meditteranean, this could see the HMS Illustrious heading to the Indian Ocean a month or two sooner than OTL. Originally she left out in March 1942, and was there to provide cover for the Madagasscar landings with HMS Indomitable.
If she can head east in January or February, she'd probably join with Indomitable and Formidable, making Force A a very powerful group to deal with, especially if she has Wildcats or Hurricanes onboard for fighter cover instead of more antiquated fighters.
It wouldn't be enough to stop Nagumo, unless they could hit him at night, but assuming Somerville is smart enough to avoid detection as in OTL, it would still leave him with a powerful fleet in being.
As for Ark Royal herself, sometime in mid to late 1942, say after Torch, it might not be a bad idea to return her to Britain or even send her to the US for a good overhaul period.