I disagree. Level 1 Q, level 2 E, max W.
Katarina isn't a super strong laner. Even poking with Q, laning phase can still be difficult. The trick isn't winning laning phase. The trick is surviving laning phase.
Then in team fights, you play her slightly differently then other champions. Instead of going for high priority targets, Katarina needs to focus on whoever is killed most easily because of two reasons:
1) He cooldowns reset on kills and assists
2) Her Q, W, and R hit multiple targets.
If you QEWR, you're dealing damage to everyone, and a TON of damage to three people. If you just finish one of these players off, it's either an Ace, or the enemy team runs away, because as soon as your R is done, you QEW again. If you finish off one of the other champs your R was hitting, you can QEW to the third low health champ. Finish that third guy off, and your R is reset. By this time, the amount of damage the tankiest two have taken just from your Q and W means that another QEWR is usually enough to finish them both off.