Hi,
I am WLAN developer with 11 years experience, I have worked in almost all areas of WLAN, developed Drivers, Firmware and Software.
I do not have experience working with drones, but after a quick search found that the WLAN module in px4 is ESP8266 and they have opensourced FW, from a quick look I can do the work of configuring and controlling the drone using the WLAN module. IIUC, we should develop a command protocol viz WLAN link on top of MAVLink supported by px4.
I have only provided a tentative duration, I can give you the proper estimate only after getting more detailed information on the scope and timelines of the project.
Please let me know if you have any queries.
[update]: FYI. I was able to checkout, build and run some tests in the JMAVSIM in my laptop, got a good idea of px4 environment.