My son will have a close to 3 month validity on his British passport when travelling from New Zealand where we now reside to the UK. We transit Doha both ways on this journey, is this short validity going to be an issue?
Since you're not clearing immigration in Doha, their passport validity rules don't apply to you.
Even if you were to enter Qatar, the country only requires 3 months validity from the date of entry.
So you will be fine