Japan was an ally at the time. So bring out 2 powerful Billy big balls Lions or Tigers or even an Orion class battleship or two and the Japanese would lose it.
They would feel a pinch and no mistake. So by sending 2 weaker Indefatigable to the Pacific doesn't send the wrong signals to the IJN.
12 inch guns were the best the Germans were doing and so her time line German equivalent was Goeben.
She wouldn't meet a German capital ship so her weakness was not that weak. Unless you end up at Jutland but that wasn't why she was built for.
Ah, so to avoid upsetting the Japanese you spend your tax money on a 2nd rate ship?
The Japanese are not likely to impressed by it.
If the Japanese in 1910 and onward do become an enemy the HMS Australia is not likely to influence them very much.
The Early British battlecruisers made a lot of claims but they were short of substance.
They may have been good for chasing commerce raiders but they weren't very good commerce raiders themselves. They either had to to 12in guns and use up ammo on freighters or try to use 4in guns, neither was a good solution. The British had accepted low elevation main guns and they increasing outclassed by other ships.
The Japanese had to two large armored cruisers that took quite a while to build, but they had four 12in guns and eight 8in guns and they could out range the Australia,
The
Ibuki-class as had fourteen 4.7 in guns which meant as commerce raiders they didn't have to use their 12in guns on freighters.
The Japanese also had two post 1905 battleships with four 12 in guns and twelve 10in guns guns.
And they had two "dreadnoughts" that were building before the Australia was laid down.
Odd balls in that they had four 12in 50cal guns and eight 12in 45 cal guns but they were powerful ships for their time (1912 which was about a year before the Australia was completed.)
One big British battlecruiser won't swing the balance but building a 2nd rate ship isn't going to impress the Japanese, especially in 1911-1913 when the Japanese can see just how fruit-loopy the British design process was. The Japanese sure didn't get sucked into those Lion fiascoes.