Yes there are size restrictions and weight restrictions to send cargo from UAE to New Zealand, if it is air cargo each airline has its own restrictions details are available on their website. If it is sea cargo the maximum size can be 228 CM x 228 x 228 if it is going as LCL but if you are planning an FCL it would be different however the width cannot go more than 230 cm and the height is limited by 260 cm
All your personal belongings and House Hold Goods can be shipped to New Zealand from Dubai, but you cannot take any DGR items and commercial items if you are planning for a duty allowance claim.
The normal shipment by Express Cargo takes 4 to 6 working days if it is ocean freight it would need a 40 to 45 days depends on the location