firstly, you don't need to take any special precautions for the little ones. There are no harmful deseases or animals on the island. There can be some moscito's, but there is no Malaria on MRU.
However, make sure that you have shoes at hand to protect your family's feet on the beach and in the sea, as you have coralpieces, urchins and some harmful fish (not very likely to step on) that you surely do not want to touch with bare feet.
You should also consider whether it is a good idea to rent a car on MRU. The street conditions vary, they have left side trafic as in the UK and there is no cost argument for a car rental. If you hire a taxi for one day, you will have to pay between 50 and 60€, depending on the distance or tour. The cost for the rental car will be around the same if you take into account that gas is available at about the same price as in Europe. And: as the driver you will not be able to do some sightseeing on the way.
My suggestion clearly is to use taxis, as it costs about the same, but it is much more relaxing.
Immer wieder gerne auf Mauritius und im Meer darunter ;-))