Can I air print to pdf instead of to a WiFi printer?

Actually you can. In the AirPrint dialog, zoom into the preview by reverse pinching the image (spreading your index finger and thumb from a touching position on screen) This will open the Preview screen.

Then tap on the Share icon at the top right corner and select "Save to Files". This will save a copy of the item being printed as a PDF in the Files App.

So if I understand you correctly, your ultimate goal is to create a PDF document. If that’s the case you do know iOS has built in capabilities to create PDF documents, right?

One way to do it is to choose Share > Print, and on Printer Options screen do a pinch out gesture on a print preview; this will open preview of A PDF document of whatever you wanted to print.

To save that document then, tap Share and either save to the Files app, Apple Books app, or email to yourself or whatever else you want to do with that PDF file.

No.

Check with the app developer and see if they have a way to help you.

What is the app you used to create the document and does it have an export feature?

I don't have that app but does it offer a means to export?