Here's a highly recommended suggestion for NZ first timers, done a few years ago but no change other than, probably, higher volume of bookings. All streams bridged and low risk of walk-closing snow in Dec/Jan. Heaviest day is day 2, graded climb to Luxmore; then day 8, graded climb after leaving Lake Mackenzie hut.
Fly to Christchurch, rental or bus to Te Anau. Confirm Kepler & Routeburn bookings at DOC office.
Night 1: Te Anau
http://www.doc.govt.nz/upload/documents/parks-and-recreation/tracks-and-walks/southland/kepler-track-brochure.pdfDay 2: Short bus ride to start of the Kepler track. Walk to Luxmore hut.
Night 2: Luxmore hut
Night 3: Iris Burn hut
Night 4: Moturau hut
Day 5: Short bus ride back to Te Anau. Remainder of day R&R and replenish.
Night 5: Te Anau
Day 6: Bus to Milford Sound, relaxing boat trip on Milford Sound, get the return bus to drop you at 'The Divide'. Walk to Lake Howden hut (~1 hour).
http://www.doc.govt.nz/upload/documents/parks-and-recreation/tracks-and-walks/southland/routeburn-track-brochure.pdfNight 6: Lake Howden hut
Night 7: Lake Mackenzie hut
Night 8: Routeburn Falls hut
Day 9: Walk out to the Routeburn shelter, bus back to Queenstown