Now don’t get me wrong, I have nothing against dirigibles. But, steam punk is a whole different genre. If we’re going to go that route, then someone should have told me that in the first place.
The fleet of dirigibles was just an example. The OP clearly has some sort of problem, which he believes can be solved by flinging a nuclear plant with a catapult. However, before we spend too much effort on this, we need to stop and determine if there is a better way to accomplish the OP's
real objective, which he hasn't stated.
We also need to consider questions such as:
Is the plant being flung
to somewhere, or
away from somewhere? What are the accuracy requirements? Would it be acceptable to dismantle the plant, fling the individual components, and then reassemble it at site? (Hurling one building at a time would help reduce the scale of equipment required).
Why a catapult in particular? Has using rocketry and/or explosives to put the plant into a sub-orbital trajectory been considered? I've already expressed my preference for dirigibles, but if the hurling part isn't strictly necessary, very large flat-bed trucks might also be appropriate.
Nuclear power hasn't been very popular lately. Why not fling a solar power installation, instead?
Of course, if hurling a nuclear plant is the objective in itself, then this analysis is unnecessary, although Brother Mythos does have some good points, and it would make sense to do a comparative study of catapults vs. trebuchets prior to proceeding.