I'd consult with your doctor or her's on this one. Not sure if getting the vaccine if you've been exposed recently poses any risk or not to your wife. I had my immunosuppressant on Thursday last week and Collin County scheduled my on Tuesday. Given my "weakened immunity at least in theory, I did consult my Doc. She decided that I get the shot. Point being, her doctor knows her best.
If you are asking more in terms of her not spreading the virus potentially, still, let her doc make the call. I was in my car, nurse administered the shot outside of the car. We wore masks and to odds of spreading the virus if I'd been a carrier were almost 0. Also, see if the administering group has any rules on that. Call them as well as there should be a number to call for any questions.
My questions are, if you are in TX, a lot of places administering the vax are closed due to weather. Where is she getting the vaccine and how do they plan on administering the shot? Like I said, if she is going through a drive through situation and her doc says its ok for her to get the shot, the nurse giving the shot will be outside. But if it is at a clinic, given quarantine procedures, doubt she would be able to go anyway.