Why are my courgetts rotting on the ends while small

This sometimes happens to the fruit when the plant is still small and lacks the resources to fully develop it. Sometimes it's because the female flower wasn't properly pollinated. I guess your plant is still quite small?
If the plant is healthy, there is nothing to worry about. Just cut off the courgettes which are rotting and the next ones which form should be ok.

I had the same problem, sometimes as the flower dies back can maybe cause the courgette to rot, so my trick is to remove the flower as it starts to die off.
I have had a few more courgettes with no problems

mrs melon x