You’re right in that it works just like other prescription/orders from your doctor.
But you do have to find a facility to administer the IVIG prescription. I’m really not sure about a mobile IV nurse as an option but again that is something to research.

What I’d do is look online. Type in the city in which you’ll be staying. Then look for “Infusion center near me”. Most often it is an infusion center in a hospital. Give them a call to see what their procedure would be to get appointments set up.

You may have to call Medicare and/or your Medicare supplemental insurance provider to find out how to submit approval for having this done. The fact that every time I’ve gone to this clinic in Florida, there are other people next to me from their respective states having the same things done, tells me it’s pretty routine.

Just doing a quick perusal online I found this site. I haven’t looked into it very deeply but wondering if this might be an option. It seems tailored to people who travel and need consistent IV treatments.
https://optioncarehealth.com/patients/infusion-therapy-care/traveling-infusion-therapy
Have you checked in with your insurance?