Hard to say.
Absent the Taiping, you probably avoid or greatly reduce the damage caused by the concurrent rebellions inspired by the example of Qing weakness. So it's doubtful there follows an attempted independence movement in Yunnan, and Taiping sympathizers don't seize Shanghai. The Qing response to the shift in course of the Huang He (Yellow River) will be less insubstantial, meaning the Nian rebellion will have a poorer start. And of course the Nian and the Muslim conflicts in the high northwest both will occur in an environment where the Qing can focus on them, rather than festering as by far lesser threats. The leader of the Nian probably declares himself Son of Heaven sooner, but I can't see him accomplishing much - the problem with revolting because you've lost everything to a natural disaster is that you have to try to revolt after you've lost everything to a natural disaster.
The trouble is that you have to eliminate the Second Opium War, which broke out mid-Taiping, or you're just going to have a different mass rebellion wrecking China. There was tremendous amount of anti-Qing sentiment in the country, for the general mix of economic and social problems, for weakness in the face of foreigners, for being foreigners, and more. Historically the Taiping burnt off a lot of the available tinder, if you will, making similar large scale rebellions both more difficult and less desirable - "Look how well that went." Without them, all that fuel remains available for a future spark. Given that a second war over opium is very likely (and will utterly humiliate the dynasty), and that the Yellow will still burst its banks, wreaking horrendous destruction....
A different rebellion, or set of rebellions, would probably follow.
So what are they like?
Well, militarily, the Taiping did benefit from many of their unusual practices, but politically pseudo-Christianity was largely a disaster. It managed the neat trick of alienating the vast majority of Chinese people that encountered it and the Europeans that might have offered it support. And of course the peculiarities of its leadership meant that they spent a great deal of time murdering each other.
That implies that there's unlikely to be a rebellion with quite as immediate and dramatic a military success, but any that makes it to the level the Taiping did will probably be more successful still.
Hrm.... Also, any rebellion will need military forces. That can theoretically be assembled anywhere in China, but the easiest place would be in the southwest, where inter-community violence meant there were plenty of local militias in place. That is how the Taiping military got started.