If you accept this distance theory to be close to accurate (1500 miles)... and you factor in that a raven can fly 60mph (or more) in the world of ASOIF, a raven can make that flight in about 24 hours or less.
The Children of the Forest taught the First Men how to use ravens for long distance communications thousands of years prior to the events of the show, and they are basically magical creatures. Ravens that can carry messages to various points on a vast continent with immense precision, including to mobile locations like army camps, and long ago were able to speak the messages that they were to deliver.
If you accept that ravens are essentially magical beasts, they can probably fly much faster than our real life versions.
The month for the trip is far more dubious.