What type of test can I do to show that water is one of the products in a neutralisation reaction?
As was written in comments, it is nigh impossible to detect the formation of more water in an aquaeous solution. Unless you coloured the oxygen atoms in $\ce{NaOH}$ pink or purple you would have no clue which water molecule is new and which isn’t.

Say you had a $1~\mathrm{M}$ solution of both acid and base and used $25~\mathrm{ml}$ each; you would create $25~\mathrm{mmol}~\ce{H2O}$ in the reaction or approximately $0.45~\mathrm{g}$. That’s just about $1~\%$ of the total water added, so you may be able to detect a slight increase in weight if you distilled away the water.

Do not try to get your hopes high, though.