In late October 1941 Force Z sailed from Britain to Singapore. According to Wikipedia, Churchill wanted a carrier in Force Z, but only HMS Indomitable was available, and only upon completion of her trials and working up in November.
But why wasn't HMS Ark Royal sent with Force Z? She was presumably available, as she was at sea and sunk three weeks later in Nov 1941. With HMS Indomitable coming online in November, and given that after Ark Royal was sunk Indomitable was still sent to the Far East, a few weeks window without either carrier in the North Atlantic should be acceptable.
What difference would Ark Royal and her >48 aircraft CAG make to Force Z? If Force Z follows its historic path up the Thai coast I'd suggest that Ark Royal and her Fulmars, Swordfish (and Skuas?) will be sunk (by a modified, fighter escorted IJA/N strike), just like HMS PoW and Repulse. But with a fast fleet carrier, perhaps Force Z would have operated and deployed differently. Keeping Force Z at Ceylon, for example would still serve its deterrent role. I'd also like to think that Ark Royal could have brought aircraft for HMS Hermes, and instead completed HMS Indomitable's Jan 1942 RAF Hawker Hurricane ferrying mission in November 1941.
Why didn't HMS Ark Royal join Force Z? Ark is just made for Pac Ops.