Well, thats a hard one to call! Im inclined to think that you probably would need their permission to do so. Im no legal expert, however I know of a few similar situations.
American airlines kicked up a big fuss a few years ago regarding people releasing aircraft for flight sim painted in their livery. Even though the aircraft were free of charge American were not too happy. Im not sure what the final outcome was, however when I downloaded the AA
pack it came with a note saying it was officially endorsed by the airline.
Personally i think the airline would object to you doing this for a number of reasons. Most importantly the airline probably already has an official calendar, and you would be competing against this for sales. I think they may also be worried that your calender may portray them in a bad way, and decide to stop you proceeding.
Whether they would take you to court or not is a different matter. You are not breaching copywrite rules, however they might argue the brand is their intellectual property and sue you for using it without permission. (perhaps if you were to make the calender about aviation in pakistan and inlude afew other airlines you could get round this, as you are no longer using PIAs image to sell the calender...)
I would recommend you email the airline and ask them for heir permission before proceeding. However I was writing a program a few years ago that used the boeing name. Even though i explained the program was going to be freeware i was refused permission. I would expect PIAs response to be similar