I'm trying to get my pet to tier 3 and was wondering if the level of the pet counts toward the total needed for the tier?

Level does not count. Just speed, defense, strength and health.

No, it doesn't. The only stats that count towards your tier total are Health, Strength, Defense, and Speed.

Just a heads up NEVER train level until you have to. This is to reduce time and costs. There's a whole battle forum for good tips to train and even the tier break downs you need to get to the next tier. Just remember you can bump stats to 2.5x that of level, so a lv 10 pet can have each stat in speed, strength, defense and health up to 25 before level training would have to happen again.

Thanks all!