Well, that's even worse. I think you have to go to solid-fuel rockets to get any earlier that.
To get a pure Dieselpunk Space would probably require a piston engine driven Aether Propeller ... of course, Aether is more Victorian Steampunk than Dieselpunk ... so I guess that a compromise will be needed somewhere along the way.
I would start with these very early pulse-jet engines for clues about TL 5 metalworking capabilities and for graphic clues about what form a Dieselpunk Rocket Engine might take.
I was looking at a three stage to orbit for manned launches ...
[Stage 1] [USS Akron]-like hydrogen airship drop launches an X1-like pulse-jet second stage at altitude.
[Stage 2] Small improved Congrave-like solid rockets boost the craft to critical velocity to start the pulse-jet. Pulse jet carries the third stage on a sub-orbital trajectory and releases it at apogee.
[Stage 3] a V2-engine rocket boosts the craft to stable LEO.
Like the saying goes, once you are in orbit, you are halfway to anywhere.
Interplanetary, I see solid-fuel cargo flights and liquid-fuel manned flights with H2O2 teakettle thrusters for fine control.
I would follow a small steps plan for travel ... Station in LEO, Station at Lagrange Point, Station at destination orbit ... special rocket from surface to LEO Station, space taxi orbit-Lagrange-orbit, special rocket orbit to surface (moon of gas giant?).
Perhaps there is an Asteroid Station to support asteroid mining?
If we get to low enough gravity, I would start to look at a tower from the surface to orbit ... or a cable from stationary orbit to planetary surface (the devil will be in the details).
Aesthetically, we get Art Deco and the Streamlined Era for structures and vehicles ... flight suits and coveralls and goggles for clothes.
[EDIT: Corrected name of Aircraft Carrier Airship.]