I'm flying QF to LHR and I'm connecting to DUB on EI on a separate PNR.

I'm flying QF to LHR and I'm connecting to DUB on EI on a separate PNR.

My question is; should the QF flight arrive late will anyone compensate for the missed connection?

I thought travel insurance would be the most likely, but I can't seem to find anything in their policies.

No, you will not be compensated for a missed connection on separate PNRs; this only applies to flights on the same PNR. If your QF flight arrives LHR too late to connect to the EI flight, EI will almost certainly declare you a no-show and not compensate you.

If you need to be rebooked, depending on the fare conditions EI may be able to put you on a later flight subject to a no-show fee.

Faced with similar situations, I've always booked a later connecting flight than I should need.  Whilst most airlines have a 2hr minimum connection time, your incoming flight only needs to be an hour late and you're stuffed.  Rather than be anxious for the whole flight as to whether you'll arrive on time, I'm happy to hang around an airport for a few hours for a later connecting flight.

And I've done that trip to DUB several times via QF & EI.  You made a good choice with EI rather than using Ryannair.