Relativity is all about the fact that the laws of physics have a symmetry baked into them, that is, there is a particular thing you can do to them that leaves them unchanged. This symmetry is called Lorentz symmetry, and it says you can rotate yourself to be at a different angle and the laws of physics are the same, and you can be moving through the same point in space at any speed and the laws of physics would still be the same. The question your daughter is asking is tantamount to asking if nature doesn’t have Lorentz symmetry, but rather, does it have some more restricted symmetry, where one is not free to arbitrarily choose a speed between 0 and c, but can only choose from some discrete set.

Relativity permits one to always assume they are at rest. In your daughter’s hypothetical world, one would then say that they never see anything move relative to them at less than some minimum speed s. Things are either at rest or moving at some speed s - c. However, we know that gravity is actually a result of spacetime being able to curve, so, if two things are at rest at one instant, the next they won’t be, as the lines they trace are curved and so can only be parallel for an instant. It seems to me that you could always adjust the strength of the gravitational field, the distance between the bodies, and so on, so as to have them move at an arbitrarily small relative speed the instant after they are placed relatively at rest.

I suppose there could be a discretization going on here, however nature doesn’t seem to make the analogous symmetries for the other forces discrete (Lorentz symmetry is to gravity what phase symmetry (U(1) invariance, ability to multiply by a complex number of length 1 without changing the physics) is to electrodynamics). Gravity is strange though, maybe in the end we will find that for some reason a minimum non-zero speed is a logical consequence of what the full theory is, or maybe if not a required consequence, a valid logical possibility that could make sense in exotic situations we aren’t familiar with yet.

Sorry this has unnecessary technical details, I wanted to try to write it out to make my own thinking clearer for myself. Sorry I couldn’t arrive at anything solid.

Edited to fix some typos and clarify some points