I found this on Wowhead;
How to make Postmaster Malown spawn to then obtain the Burnout Battle Pet.
In order to do this, you must find a letter which is hidden inside one of different spots in Stratholme Battle Pet dungeon.
The letters may appear at several waypoints.
They are being listed in order of starting at the beginning of the run to the end.
It will make things easier if you search as you go along with your battle.
Some of the spots will not be accessible until you defeat an opponent near the area.
/way 68.9 54.0 Letter
/way 59.7 40.6 Letter
/way 57.8 36.9 Letter
/way 56.9 50.8 Letter
/way 48.6 24.9 Letter
/way 40.2 10.4 Letter
Once you’ve obtained the letter go the area where Nefarious Terry is,
/way 57.8 13.6 & Postmaster Malown will appear.
You have 20 minutes to fight him after which time he disappears.
FYI Xu-Fu Pet Battles site has the tried & best grouping of battle pet teams to do this fight easily.
Beating him rewards you the “Malowned” achievement & the pet “Burnout” will be instantly added to your battle pet list.
Happy Hunting & good luck!
From what I remember, the letter might not always be there, I think it took me 3 or 4 runs to find it. But then again it wasn’t that easy to spot so I might have just missed it the other times.
Edited to add, also found this tip;
You can just enter the pet dungeon, check the 3 spawn points that are available right from the start, and if the letter isn’t there, just leave the instance and restart. Took me about 5 restarts to find the letter. You do not have to do any pet battles to find the letter. This way you can easily ensure that you can spawn the Postmaster during your run.
Note: Once you actually battle him and fail / run, then you won’t be able to find the letter after restarting the dungeon.