I think he’d stay around a little longer than that, from memory the ‘faceless men’ were broadly people who were elected in the 2007 Ruddslide, so I think they could be butterflied away and Labor could go into a place where they more or less had a steady hand over the leadership (don’t forget that Beazley was Labor leader from ‘96-01, Labor can believe in their leadership if they want to). My prediction would be, after winning ‘04 with a fairly large majority, he’d get a reduced majority in 2007, and it’s anyone’s game in 2010.
As for his Prime Minister-ship itself, I don’t think Latham would be as bad as he is now in OTL. I’d see him as more centrist than the far right that he’s become, with a strong focus on public services like schools and hospitals, whilst simultaneously helping middle to low income earners through tax breaks. There’s be a decrease in defence spending, given that he was very keen to get ‘the troops home by Christmas’. There’d also be a frostier relationship with America, given Latham’s feelings towards Bush.
But ultimately, Latham’s strongest weakness is that he can’t trust people. His diaries are full of paranoia towards prominent Labor frontbenchers, like Rudd, Swan, Smith, Beazley, even Crean. I think he’d just about be able to cope for his first term, but when the GFC hits, he’d foul that up massively by refusing to follow advice when it was most needed. He might have gotten through it unscathed. But that would require a major change in his personal philosophies, which I just don’t see happening.
Post-Prime Minister Latham would definitely be a different beast to OTL Latham. The Latham Diaries make it quite clear that the start of his downfall was that his anger came from not being in power. There’d be a memoir where he insults people who he’d believe lost him the Prime Ministership, and maybe a high profile ‘no holds barred’ interview, but after that, a likely retirement into private life, only popping up to endorse Labor at election time.