Note- this is not necessarily what I think would most likely have happened if the Taiping had won... but it's my best attempt at a scenario where the Taiping not only beat the Qing but also are a success afterwards...
POD: 1853. After taking Tianjing (Nanjing), the Taiping do not make the mistake of pausing to consolidate their gains, but instead keep going to Beijing. The Qing are overthrown, and Hong Xiuquan becomes Tian Wang (Heavenly King) of all China, now officially renamed Taiping Tianguo (Heavenly Kingdom of Great Peace).
Initially, private property ownership is abolished, all land is held and distributed by the state. Civil service examination is changed from the Confucian classics to Hong's version of the Bible, which includes a third grouping of books written by Hong.
Taipingism differs from mainline Christianity in that it is anti-Trinitarian (Jesus was created by God), and teaches that Hong was Jesus' half-brother.
Note: I'm not sure if Hong believed that he was literally divinely conceived, or whether he only meant Jesus was his brother in a figurative sense. I recall reading somewhere that Hong also claimed the early Chinese emperors were also Jesus' brothers?
Hong's rule, which lasts until his death in 1880, is somewhat like that of Mao, only a century earlier. But despite Hong's craziness, China actually does better during the 1853-1880 period than in OTL, since there isn't a 12-year long Taiping rebellion with resulting economic devastation and 20-30 million dead. And from around 1860 onwards, Hong's chief advisor Hong Rengan implements the Meiji-like modernization program he intended to implement in OTL, which includes a reintroduction of private property and establishment of Western banking system.
Taiping China is unpopular with European powers, who naturally consider Taipingist Christianty a heresy, and the British resent the Taiping abolition on opium. However, the Taiping are better able to resist the Europeans than the Qing were in OTL: Their armies aren't largely tied down fighting a huge civil war, and they are much better-motivated than the Qing forces were.
A Western expedition might still be able to march to Tianjing and burn Hong's palace, just as the Anglo-French forces marched to Beijing and burned the Qing Summer palace during the Second Opium War of OTL. But it would be considerably more difficult, and when the Westerners reached the capital they wouldn't find anyone there willing to sign a treaty with them: The Taiping leadership would just relocate, while their forces continually harassed the invaders until they eventually gave up and left. Unless the Europeans are willing to undertake the major effort of occupying and pacifying all of China, the Taiping regime will survive and continue to pursue modernization (although one thing they can't do, without Western governments permitting it, is construct a modern navy, since Western navies have complete domination of China's coastline).
After Hong's death, he is succeeded by his son Hong Tianguifu, and the dynasty continues to the present.
In this TL, the late 19th-century annexations perpetrated by Russia in OTL do not occur, the Sino-Russian border remains as it was defined by the Treaty of Nerchinsk in 1689, with China's territory including all of Siberia. Hence, Taiping China is the world's largest country in land area.
From 1860 to present, Taiping China's average GDP growth rate is more than double that of China in OTL over the same period. So by 2008, Taiping China's GDP is about 2.5 times that of China in OTL: The world's second largest economy (after USA) at market exchange rates, and largest when adjusted for purchasing power parity.
TAIPING CHINA IN 2008
Official Country name: Taiping Tian Guo (English: Heavenly Kingdom of Great Peace)
Usually referred to by Chinese as simply Tianguo or Zhongguo (Middle Kingdom).
Population: 1.1 billion
Capital: Tianjing (Heavenly capital)
Government: Authoritarian monarchical theocracy
Religion: Official state religion is Chinese Christianity. Head of state Church is the Tian Wang.
Economy: Free market
Currency: Yuan
GDP: $8 trillion
GDP (PPP): $16 trillion
2007 GDP growth rate: 4.5%
Military budget: $400 billion (5% of GDP)
Active troops: 2.1 million
Strategic nuclear forces: Approximately 2,000 strategic warheads, level needed to ensure no other nuclear power has significant strategic superiority.
Space program: Re-usable SSTO shuttle, manned space station equipped with Earth-Moon shuttle, manned moon base.
Space program budget: $80 billion (1% of GDP).
TIMELINE
A detailed world timeline, from POD to present, is something I could use help with.
A few general observations:
Probably no major historical changes outside East Asia until about 1880s at the earliest. However history of Japan and Korea, possibly other parts of east Asia as well, may diverge significantly before 1880s.
If there is any late 19th century Sino-Japanese war over Korea in this ATL, China will have superior land forces (equal technology and trainng, superior numbers), Japanese Navy will be either superior, or at worst about the same as China's. Result: Certainly more favorable to China than 1894 Sino-Japanese war of OTL.
Not sure if there is any circa 1905 Russo-Japanese war in this TL.
Butterfly effects mean if there is still a circa 1914 European Great War, it starts a little differently than in OTL, and unfolds differently as well. Which side, if any, does Taiping China ally with?
Bolshevik revolution is butterflied away, USSR never exists.
Suggestions?