It's physically possible to do this--I used to live in a place where the downstairs powder rooms were 60" x 60", so stupidly large for just a sink and toilet. A lot of my neighbors put in showers and a 34" corner opening shower worked the best, but it was plenty squishy with any shower. Going in there involved a lot of walk-like-an-Egyptian.

However, that was totally not to code (no professional plumber would touch the job), and your room looks even smaller. I doubt you can legally do this. Perhaps it would be possible to make it into a wet room?

You will constantly hit your elbows with a 36" shower. Plus, your layout will not pass code requirements. You need a minimum of 24" clear space in front of the lavatory and toilet. That 18" between the two ain't gonna cut it.

You might look for one of the toilet/sink combo units, but those are spendy. And you need more space at the side for that. 48" would be the minimum I'd think that you could have to access the basin on top of the toilet. Do that by eliminating the shower itself and adding a floor drain wetroom, and I think you might squeeze everything in and still pass code.

live_wire: toilet and sink are existing, so we get a pass in our jurisdiction.

And if any one complains: the toilet was installed in 1950, and roughed in at 12". There is enough room to rotate it making for a 24" clear rectangle in front as measured from each toilet edge.

The toilet/sink combo unit can be added for $120 (see the link)

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But the real question is elbow room. What sizes have people showered in that worked or were too cramped?

Our bid for the simple version is already $12k, wet rooms we assume would add a bunch.

Here is a link that might be useful: Toilet Topper SInk

Brycenesbitt: We have a corner shower like the kind you are describing. It's closer to 38" instead of 36", but we don't bump elbows, shoulders or anything else. While it's in our guest bathroom, we used it ourselves for four months while our master bath/bedroom were renovated. I do realize that with curves, adding 2" to the radius makes a real difference, but I would think that a 36" would be very doable.

My sister has a 32" square corner shower in her guest bath. And, there we can bump elbows. If we're careful, it's not all that bad -- and neither of us is what you'd call svelte! I wouldn't want to use it every day, but for a few days at a time, it's just fine.

I've showered in a couple, one of which was, I think, more like 32". That one had a sliding door. The larger one had two opening doors that met in the middle. It was adequate for one. Both showers had handhelds, which is useful in a small shower. The larger of the two also had a rain head and two body sprays.