If you're just worried about temperature, tepid sponging and paracetamol (ask your doctor regarding dosage).

Going to paed is a bit overkill, really.

Of course, but I think TS specifically mentioned wanting to go to a paediatric specialist, and not wanting to see a GP at all.

During non office hours, the ones on standby at hospital are usually emergency and O&G docs. If baby is in danger (not breathing, temperature too high, having seizure or needing resuscitation), the emergency physician will handle the case, not a paed.