Our house master bath has a pony wall around the toilet and we want it fully enclosed with a door. Any recommendations on contractors to do this type of work in Houston area?

Pretty much any drywall contractor could do this. Doesn't seem like a very challenging job.

NextDoor.com will bring help
Can't say if Home Depot services get good reviews there or not.

As designers, we usually steer away from enclosures that may bar future wheelchairs from entry/use.
A pony wall can be heightened, see-proofed EZ DIY
A folding screen sells everywhere
A 2nd ceiling exhaust vent can be done.