I'm up early myself today, tuned in at 1000 UTC to hear the news, followed by "Double Vision" Foreigner. It's their Saturday Night request show on their national channel, which will sadly switch off at 1100 (the program runs til 1200 but RNZI goes to a different stream at that time).
EDIT - it appears that New Zealand has gone on summer time, because they have a Facebook group for this show and it shows that Foreigner was leading off their 11:00pm hour, meaning they're UTC+13 now. So nothing will be missed by SW listeners now. Huzzah! Currently playing "Tubular Bells" Mike Oldfield (1021z).