No, that sentence is not grammatically correct. Availability is a noun meaning how much of something is there to be used. You could say "What is the availability of this job?" or "Is this job available?" or "Is this job still open?"
"The promptness of delivery of your order is subject to availability in our warehouse."
I need to inquire about the availability of the product.
You are too late to start this job.
I am reading the job description now.
He rang the hotel to see if there was any availability next weekend.
You are unqualified to do that job.
Due to the shortage of doctors, the job availability for a doctor is great. There are many fields a doctor can practice in.
Example sentence - His first job was in the retail industry.
My current availability is to have a stable company and stable job that I can work and learn more to the extent of my knowledge and availability
the citizen applied for a job.
I decided to seek out a job.
I applied for a job this summer.