non-EU country -> Ireland with my dog. Any recommendation on flight routing?

Hey all! I'm readying for my relocation on upcoming June~July with my dog. South Korea -> Dublin.

After a bit of research now I know what to prepare especially for the inspection process. However, one missing piece is the flight option.

Initially looked up Lufthansa group, and according to the customer support (both phone call and live chat) they do not accept animals for the flights to Dublin. Due to the absence of 24-hour animal inspection personnel at the airport.

I'm checking other options as well though, thought it'd be good to ask some personal experience here, if possible.