You could theoretically make a steam-powered airship, but it wouldn't be worth the hassle. Moreover, by the time that we had the technology to make the airship frame itself we already had very good diesel engines.
The efficiency of a plain old non-compound Watt-type reciprocating steam engine is about 2.5%. For an airship you want a condensing engine, because you absolutely want to minimise water loss. Water is heavy.
Stephenson's Rocket locomotive of 1829 weighed 4300 kg (complete with water in the boiler). You need at least two engines, unless you plan to have some fantastically complicated transmission chains. Let's say that with a little better engineering you can reduce the weight to 3 tons per engine.
The first commercially sort-of successful airship, the Zeppelin LZ10, was 140 meters long, had 17800 cubic meters of hydrogen and could carry 13 crew and 20 passengers; it was powered by 3 engines of 100 kW each, with a maximum speed of 77 km/h.
Say that your airship will use 2 light-Rocket style engines, souped up to give 100 kW each, and you want to have enough fuel for 5 hours; suppose that you burn some kind of coke or anthracite giving 30 MJ/kg. The two engines will weigh 6 tons, and you need to carry about 5 tons of fuel. You need 12 tons of lift only for the engines, water and fuel!
12 tons of lift require 12000 cubic meters of hydrogen. The ship structure will also require lifting, plus any passengers. Overall, your ship needs to be much bigger than LZ10; say, 180 meters long, 34000 cubic meters of hydrogen.
And from here comes the fundamental problem: what material are you going to use for the ship structure? The airship cannot be a blimp, because if needs to lift those heavy engines, water and coal: it needs a rigid structure. The structure cannot be made of iron — too heavy. Cannot be made of wood — too weak. You need aluminum. But if you have aluminum, why are you playing around with steam engines?
The second big problem of using inefficient steam engines in an airship is the loss of weight. Every ton of coal you take on board at take off and burn requires that you vent 1000 cubic meters of hydrogen in order to remain in equilibrium with the displaced air — airships are aerostats. When you land, you need to refill the gas cells, otherwise you won't be able to take off again.
The third problem is the nature of steam engines, which burn their fuel in the open, which is a big huge enormous hazard for a hydrogen-filled airship. (Cannot be filled with helium, for reason of the need to vent lifting gas to compensate for the stupendous loss of weight given by burning coal with a very low energetic efficiency.) Real life zeppelins used diesel engines, because they don't need sparks...
P.S. The picture in the question is fundamentally wrong, in that the gondola is way too big. Look for example at LZ120 (better pictures at airships.net) for a clear view of the relationship between the body filled with lifting gas and the gondola.