Considering one of the big issues the Liberal Party had was being in power from 1905-1918/1922, which left the party torn in several ways and gave Labour a big opening, the way to have this happen is to have the Liberals not be in power for so long, and this can be done two ways:
Either Balfour wins, or the Liberals loose in 1910.
For the first, Balfour's ploy actually working and the Asquith screws the pooch over the Dunglass Compact, with H.C.B resigning outright and a Liberal Party rife with vicious infighting loosing in 1906. This would take Asquith out of the picture, and with the Liberals on the Opposition, they would be able to work with Labour more effectively. With a reflective period on the Opposition, they may decide to continue the Gladstone-MacDonald Pact, but turn it into a much broader alliance with Labour in an effort to beat the Tories in the next election. If they win, then the only issue is the potential of the First World War; this may and likely will be butterflied by Balfour's winning, but a major War is going to have the pacifistic MacDonald in knots and may break the Pact or his Party.
Alternatively, the Liberals loose in 1910, and have the same reflective period and renew their pact with Labour. The Conservatives run the show when it comes to the War, resulting in the Liberals not being tarred by the war and the fractures it caused, and with Labour could present themselves as a viable post-war alternative. "We won the War, now lets win the peace!" and all that.
Basically the Gladstone-MacDonald Pact has to become the official policy of both parties for an Australian style LibLab, and those tow scenarios, whilst sketchy, are the best I can come up with.