Okay this is my current version, but I can edit it if it isn't close enough to actual scale.
Width is obviously given. The adapter is 0.5m (I'm giving you the closest SFS proportions). The silver band 0.5m. The engines protrude 0.75m, so your choice to round up or down. 1m would look good. The fairing is 4m tall. The 2nd stage is 6.5m tall (the black part I mean) and the 1st stage is 12.5m excl. engines.
This is my current draft version, Exploded view and Assembled view. I think I got the sizing a bit out. I seem to be able to make 0.5m high tanks, but I am not sure about 2.5m high Ion drives?
Looking at the prototype which is painted white, I think stage one is three rockets bolted together and is the 12.5m section below the silver band with the AU flag.
The black section above the silver band, 6.5m would be the second stage, and perhaps the engine for the third stage is hidden in the top part.
The white fairing 4m, is probably Payload and the Tanks for the Third stage. Given the width, I suspect the tanks are shorter and wider than the prototype?
To get 1.5m wide weighing 300kg with 2m high satellite imbedded, the payload needs to be about 1.5mx2m. I can make the payload a different shape to fit inside a fairing, but I fear the fairing will not detach once I break the separator. Is is less than 1m away, so the game will assume it is integral to the payload.
The main aim is to get the payload to the desired orbit, and make it look as similar as possibke to the IRL rocket. So if the fairing doesn't separate, I don't think that is a big issue.
I just need to redesign with the actual sizes now.