Well if you where abled to get to Mooshu then I assume you are not to low of level for it. Mooshu has a lot of go here to kill X NPC's and collect Y amount of things, and return to quest giver quests. On a busy day you will have others doing the same quests you are, so jumping in on someone elses battles are most likely to happen.
Nothing wrong with playing to fast, but bear in mind once you cap out then there really is nothing to do, so enjoy it while you can.
Yes, you're playing too fast. You're skipping a lot of the side quests. Because you're a Life wizard, you can get away with that better than some other schools can. It's also easy to get by if you play in groups all of the time.
To give you a reference point, I just finished Krokotopia on my third wizard, and I'm level 28.
You should backtrack through Wizard City, Krokotopia, and Marleybone and do all of the quests that you missed. Doing that will add several levels to you. Getting those levels will give you:
1) More Health and Mana.
2) The "Centaur" spell and its 550 damage at level 33.
3) The ability to buy level 35 Life gear at the Bazaar and the crowns equipment in Mooshu.
4) Possibly some spells you missed through side quests.
5) Possibly up to 3 Zeke training points if you didn't do his Troll, Beetle, and Cat quests.
6) Plenty of drops that will give you gold to buy better equipment.
sounds like you skipped a lot of side quests to get there. While side quests are extra curricular activities, you are only hurting yourself by not completing them and leveling to the point that you wonder why the big guys in the next world is picking on your poor little wizard :)
You can try to go forward as a challenge, but before you start bugging your friends for help in street fights consider going back and doing some of those side quests to level up.
That seems a bit quick to be in Mooshu, given the stats that a 30 level player has, it can be done and worked through, however, I would suggest going back and completing some quests you have missed, even Grizzleheim to level up a bit to help you out both in health and mana boosts from leveling but also spells in accord with the opponents you will be facing in Mooshu.