How to copy filename and paste as text in Photoshop

I have about 1500 files each with a unique filename. For each image I want to copy that individual filename and paste it into the document as a text layer at a certain location say .25 inches from the bottom right corner. I need it as a text layer as I still need to change minor things.

It would be great to choose the font and size. I also want to be able to copy the file type  if possible. So it would be "filename.png"

I have Photoshop CS5 & CS6. If this is easier with another program like InDesign let me know.

Thanks!