Can a 1-dimensional signal be in a domain other than the time or frequency domain?
Really, there's nothing special about time and frequency domain.

The math doesn't care whether you're transforming amplitude over time, gravel over mountain height, or smell intensity over fridge temperature. To the math, you map elements from a function space to elements from a function space when you do the Fourier transform. Full stop.

Any scalar physical entity can be used as basis for a 1D signal. Spatial signals are the most obvious: what's the height profile of something over distance, or the temperature over distance, or color over distance, whatever over distance. In some contexts, the resulting entities are called "spatial frequencies", but sometimes something else. Names are just names.

Or what is the temperature of something over pressure? That's another 1D signal. And it makes a lot of sense to Fourier transform it, if you're dealing with compressible media in a container, things will oscillate, and not necessarily over time. Do I know whether that has a name? No. Did some PhD give it a name in his dissertation about pressure in containers? Pretty likely, if you ask me. Does that name matter to anything but the notation in that dissertation? Maybe. Maybe not.

Very commonly observed: impulse / state space its Fourier "dual" location space in solid state physics.

We can go on with this all day, because, as said anything can be a 1D signal, and some have Fourier transforms with special names, other don't. It's by pure coincidence that you've heard of the time/frequency pair first. If you were a math student, you might have heard about probability densities and characteristic functions first – yet another 1D signal/FT pair.

So, really, to cite someone I think Tukey,


  One can Fourier transform anything – often meaningfully.


Your question is just asking for an arbitrary list of names. Names don't actually matter – they just make it easier to communicate about something. Whether I call something a "time signal" or a "frequency signal", however, makes little difference. For all we care, I could be calling it "original space" and "image space" (under the Fourier transform), because that's what "time" and "frequency" are. It's just convenient that these two have a name.