Hi Cath,
You can take wooden items into NZ, but the crucial thing is to have your dresser checked for woodworm and other beasties. MAF will go over it quite thoroughly I would imagine, especially because of its age. Usually they are averse to any untreated wood which might harbour the odd nasty, but, if your dresser is treated and free from suspicious holes and other signs of insect invasion, I'd hope it would be OK.
There's a bit about the MAF procedure
here .