Where to place the vapor barrier in a sunroom floor
The vapour barrier's task is to keep inside moisture away from the insulation and framing where it could condensate and create mold.
In your proposal your hot/cold interface induces condensation on the side of the vapour barrier where the insulation is.
However, you want the condensation and insulation on opposite sides of the barrier.
Your sunroom floor can be insulated as follows, with the following layers from top to bottom:

Flooring (finished flooring)
Vapour barrier
Sub-floor and framing
insulation between joists
Building wrap (optional)
Sheathing (PT plywood) with air gaps. Sheathing doubles as cladding and protects the entire assembly from rodents, abrasion etc...

(To be clear, this is the order of layers. Of course, this is not the order in which you'd build &amp; assemble it)
The above has the plywood sheathing as the bottom layer since the aesthetics of the view from-under don't matter in your case.
If, however, if you wish to finish the bottom with something like a soffiting, you'd put the optional building wrap between the sheathing and the soffit:

Sheathing (plywood) with airgaps
Building wrap (optional)
Cladding/underside finishing, breathable

If you plan to cool the sunroom (e.g. with A/C, in the summer), then the moisture from the ground may become a problem if there is insufficient air flow underneath.
In this case you will need to add a vapour barrier / retarder to the ground with rocks over it, or pour a slab. A layer of rocks over landscape fabric could work too. A barrier keeps the ground moisture away and inhibits the growth of weeds. Weeds can reduce the free airflow and also draw-up moisture.
The rocks help prevent rodents from nesting under the sunroom. Don't dig a bed though, as this may cause water pooling.