I've been playing since November and... well, it's the primary reason I haven't been posting much (not that I ever did).
I'm still hooked on the game, and it's gotten even better since I hit level 60 and joined a good guild. We raid often and have several server-first kills (including Ragnaros). We have Molten Core, Onyxia, and Azuregos and Kazzak on farm status, and we're making good progress through Blackwing Lair.
Really, I can't say that I get bored with the game, even when we're not raiding. I play on a PvE server, but we still have a fair amount of PvP activity with Battlegrounds and random city raids. I also will go back to the 5-man instances sometimes (Stratholme is still my favorite) to complete quests I missed or to get supplies/items that I need.
And yes, Alchemy is definitely a good profession. I'm an alchemist/herbalist myself, and I like being able to make potions for nearly every situation the game throws at me. The transmute part of alchemy is also very useful, especially if you want to help with making weapons (arcanite, for example) or get essences for enchantments.
If you find yourself getting bored as you get near 60, then I suggest getting into a good guild, or starting your own. Your skill (and professions) will be put to better use when you have to team up with others more often, in a raid or otherwise.