Korea, even though a wealthy country, isn't that powerful enough to unify all of china. But i wish that my country could help in taking it down.
Well, while historically Korea has been independent of the Qing, they does exist as Ming vassal state... and now Japanese Vassal state, with Joseon dynasty of Korean Kings now being formal Vassal under Emperor of Japan, and aside of the royal stuffs, Korean peninsulla is now treated as inseparable, core provinces of Japan, with Japanese citizenship being universal, with those of Korean descent having same rights and responsibilities to those of Japanese Isles, and also coastal Chinese descent.
Lets face it, Japan is THE SECOND BIGGEST NAVAL POWER after British Empire back in early 20th century, and right now with US ascending, still being the second biggest after US with British end up in the third place. It took US and British joint operation to "Salvage" Republic of China from being outright conquered by Japanese Empire, and the Qing Emperor Puyi does seriously considering kowtowing to Japanese Emperor Hirohito at 1934 peace conference (he didn't because last moment backup from Russia and Germany). If not because of European backups, once Japan gained fealty of either South or North China... the others will fall and probably Mongolia and Tibet will end up returning as well (French Vietnam is another story).
Now speaking of Korea... the very same kingdom who asked Japanese help in exchange of vassalage... instead trying to going solo and unite China? It does took a very specific series of events to establish Qing Dynasty IOTL, so while somewhat far fetched, it is definitely possible with prequisite of Korean army being modernized and become far stronger in 19th century.