Even with carry on its going to be very tight, you could try T3 to T2 airside transfer bus and use T2 connections to pass through security and immigration and get the boarding card if needed at the transfer desk. That would be faster than clearing immigration in T3 and having to landside transfer. Under ideal conditions thats at least 40 minutes.

What flight number is the booking under?

The confusion is the last flight in the current schedule from LHR arrives DUBLIN at 2205

The 2200 183 departure is Summer season only and only Sunday other its 2110