I'm not sure how 'oxygen' works- is there a tank that could run out? tubes to change? batteries to charge and carry about? I'm sure some training would be needed.

I would want training or at the very least a meeting with the baby's GP and/or Consultant and a signed letter to say I had been informed of what I needed to do.
I would also talk to my insurance company to make sure I would be covered. Our local authority has a care plan form we can complete. I've completed one for a child with asthma.