Leveling a character quickly in World of Warcraft is definitely a different occupation than developing professions.
The benefits of professions at the early levels are so lacking that it makes sense to level a character, then level the professions needed for raiding at max level. The time spent developing professions at early levels is better spent on leveling itself, rather than on professions. If the goal is to level as fast as possible, professions are time-wasters, not efficient.
Here are the professions and how they offer little help to characters at early levels:
First Aid: Helps with healing out of combat, but lacks much use in combat, because a hit stops the action of healing. Can be used with a stun skill to heal a bit in combat. Buying or finding food is just as useful for healing out of combat. Totally useless for self-healing classes, and it depends on the availability of cloth, which drops only from humanoids.
Cooking: Offers a small buff, starting at 2 stamina, for better survivability, but it is such a small amount that it doesn't live up to its potential. If you spend the time to level cooking with fishing, it can offer more substantial buffs, but that takes a lot of time, which could be spent grinding for experience.
Fishing: Standing next to water watching a bobber is a time-waster for sure. The only benefit for leveling is to use it to develop cooking.
Skinning: Can produce leather from animal bodies. Leather can be sold on the Auction House or used in crafting professions, especially leatherworking. But the time spent skinning can be performed on alternate characters, leaving a leveling character free to grind.
Mining: Can produce ore and metal bars from nodes. Ore and bars can be sold or used in crafting professions, particularly blacksmithing and engineering. But the time spent mining can be performed on alternate characters, leaving a leveling character free to grind.
Herbalism: Can produce herbs from plants. Herbs can be sold or used in crafting professions, like alchemy and inscription. But the time spent herbing can be performed on alternates.
Blacksmithing: Can make mail and plate armor, but quest rewards and drops tend to be good enough for leveling. Slight improvements for weapon damage can be made through buffs in sharpening stones and weight stones, but the benefits are not all that great. The real benefit is in the upper end, when the blacksmith can make slots for gems. High-end crafted armor and weapons are not better than what can be found in the game.
Jewelcrafting: Can make jewelry at low levels, but quest rewards and drops are better. Can make gems starting at Burning Crusade levels (around character level 60). Gems made at high levels are a lot more valuable and can be a money-maker by selling high-end gems on the Auction House. Jewelcrafter-only gems are valuable for raiding at max level.
Leatherworking: Can make some armor and enhancements, but only high-end enhancements have any value for selling at the Auction House or use for raiding. Value for raiding is less than for other professions.
Inscription: Can make glyphs for any character, but, by design, the scribe can only make a limited number of minor glyphs which might be useful at low character levels. Leveling the profession is done by making major glyphs, while minor glyphs are made by research which has a long cool-down and therefore is time-consuming. A leveling character might as well buy minor glyphs at the Auction House.
Engineering: Has little use for a leveling character, except in making bombs to enhance combat. The crafted items and enhancements have some use at the high end for raiding. The fancy mounts are only cosmetic.
Alchemy: Has little use for a leveling character, except in making potions and elixirs, but the buffs are very small and not necessary for leveling. Health and mana potions do drop from kills, but leveling does not depend on them, given the way the game has been changed as Cataclysm approaches.
Archaeology: The Cataclysm profession has some promise, but the enhancements probably will be the same as previous professions, not offering much benefit to leveling. The greater benefit will probably be for raiding.