The compressor coming on and running for a little bit and then shutting down is called "short cycling." It's typically caused by low refrigerant but can be other things as well. You're going to need a refrigeration mechanic.

The situation you describe is not normal. You need a service call from a qualified tech to check this out.

IMO

If the heat pump is a year old then it is still under warranty. Have you called the company who did the installation? What was their response?

I just had a problem with one of my units going dead for an hour or so then comimg back to life and operating normally. New unit too! The condensation line was blocked near the end of the run and the pan was filling up shutting the system down,like it's supposed too. Then it would slowly drain, the float would drop letting the system re-activate. Maybe?