Thank you for all your comments! I agree with earlier posts that China would most likley prevail against the Russians, but may find itself getting more than its bargained for in terms of increased territory and outside influences, be they military or economic reforms. One things is for sure - that was China's "last true" chance to settle things with the Russians when it comes to power projection. Starting from the 1780s and all the way through late 1960s, China's history will be one of setbacks, internal rebellions, reversals of fortune and foreign domination. Its interesting - and tempting - to assume that had China exerted itself in the 1750s, it may have partially avoided the fate of OTL.
In OTL, China's population and economy continued to expand till the Taiping Rebellion of the 1850s. If China was to secure Siberia and Far East from the Russians and if it were able to partially withstand Western interference in its affairs, the world may well have had to cope with a rather agressive and expansionist new power. That, of course, would also depend on Qianlong's successors. I would love to see a map of this alternate, Siberia-controlling China!