It is said rowter in the IT field in Australia and New Zealand.
Route however, depends on a number of things - which part of NZ/Au you're from (and hence the speech patterns prominent to a local area), how you were taught at school and under which system, industry you work in, etc.
I was taught it was 'root' at school, but on entering University was quickly corrected to 'rowt', which was (and still is as far as I know) the correct pronunciation for the geographic industry I was in. Road networking was referred to by rowts, not roots. Roots meant 'those things in the ground that feed trees' or.... well - you all read nfic.
It does bring up the interesting issue of speech patterns though.
I remember being in the US once and when I was asked where I was from I said Auckland "ork-land' but people kept thinking I was saying Oakland... despite the fact I really don't think my kiwi accent remotely even passes for any US accent.
