Add a solid border without changing the overall size

[Ofnuts]

Layer>Transparency>Alpha to selection, and do something with the outline of that selection:

• Select>Border and bucket-fill: easiest, but you don't get sharp angles
  
• Edit>Stroke selection (in Line mode, because using a brush will also prevent sharp angles)
  
• Select>To path, Select>None, Edit>Stroke path: somewhat cleaner than Edit>Stroke selection
  

All these techniques create an outline that straddles the current border of your object. You can improve on them to keep the very same outline (the painting is done only inside) or to keep the current shape (painting is done outside) but there are small details that need to be taken in account for a correct result.

The  "Stroke path" method (in the three modes:  over, inside, outside) is used by my ofn-outline-layer script that you will find here.