Level with a pet if you can because it will help keep you safe. If your pet is tanking all of the damage from the enemies you’re fighting, you won’t have to. The other reason is that pets are easier and cheaper to heal than you are. If you don’t have a pet, make sure you know how to use your defensive abilities. You can’t level quickly if you are dying all the time.
Given these facts, there is absolutely no reason to level professions with your character unless you want to "experience" leveling them up. That's up to you. Increased mount speed and flight @ level cap will make the process much faster. The gold you gain from leveling is more than enough to purchase flight training. Be sure to gain rep with your appropriate capital (Stormwind or Orgrimmar) to get a significant discount on flight training.
Created by Blizzard Entertainment and based on the Warcraft series of RTS games first released in the mid 1990s. WoW expanded on the early Warcraft single player franchise and is now a vibrant multiplayer online world, where players may engage in roleplaying, PvE, PvP, dungeon instances, battlegrounds, arenas, and raids. WoW has received four different expansions so far, including The Burning Crusade, Wrath of the Lich King, Cataclysm, Mists of Pandaria, Warlords of Draenor, Legion, and the latest expansion Battle for Azeroth and is still going strong with another expansion in the pipeline.
The leveling experience for the Burning Crusade and Wrath of the Lich King levels of 60 to 80 has been greatly reduced from 6,689,030 XP to 4,412,600 XP which is a reduction of 34%. This has been a notoriously lengthy leveling section, and this reduction will be very noticeable and appreciated by those players leveling new characters such as those allied races!