In which case you gained your false etymology from a false source, I'm afraid, Jennie. Pompey is certainly a nickname for the city, the football club, and presumably for the inhabitants and / or sailors, but your etymology is nonsense, sorry. I'm not a professional by any means, but I am a very keenly interested amateur. From the linguistic p-o-v, it's inconceivable that the second p in pompey would simply be dropped in the timescale. A p sound might evolve to or from a b, but it doesn't simply disappear or turn into an m in a hundred years.

The origin is not certain either of pommie or pompey; there are several theories for each; but the earliest recorded use of the former dates to around the end of the 19thC; for the latter, there are a couple of theories that would place its first use around the end of the 18thC (I can't find a firm date, even decade-wise, as to its first use). There is absolutely nothing that suggests any link between the two. I could go on about penal transportation, for example, but you probably already think I'm rather snottily trying to lecture you (which impression I'm trying to avoid giving, probably unsuccessfully!).

Go and have a hunt for yourself. If you can find anything at all that indicates a link 'twixt pompey & pommie, I would certainly be interested in seeing it. I cannot find anything myself...

(This covers all of the major theories as to the origin of Pompey - I'm inclined to discount the 'pompier' theory on the grounds that there's no reason why it should have become peculiarly attached to Portsmouth only.)