Do Kiwis have to pay tax during the first year of arrival in Australia?

You will have to pay tax either in NZ or Australia. This depends on whether you are deemed to be a NZ or Australian resident for tax purposes. If you are moving here for 'good' you will almost certainly be deemed to be an Australian resident for tax purposes and all your income will be taxed by the Australian government. If so, say hello to Capital Gains Tax!

Capital Gains tax? Do you pay this on your income that you would earn from employment or just on things like houses, cars, boats, etc, that you would sell for a profit?

CGT is payable on assets that appreciate in value. You do not pay CGT on money you earn as income (although the gain in asset values are added to your income for the tax year to determine your taxable income).