The players are currently at 2nd level, soon third. We are playing a campaign with high mortality. I was thinking about creating backup character as an awakened wolf. From what I read, the class levels for such a character would be the party's average level - CR of picked race. The wolves have CR 1, but have incredibly low intelligence. I decided to pick an awakened wolf, but I am not sure what should be it's level adjustment. The +1 LA from a normal wolf, who cannot speak, and neither use items or wield regular gear is a pretty tough penalty, would it's awakened version be +2?
Pathfinder has no level adjustment
That is a mechanic from D&D 3.x, which wasn't ported to Pathfinder.
You will notice that Drow, which had a LA in 3.x, does not have it in Pathfinder.
That said, a wolf is a quite ordinary creature in terms of ability scores and special abilities, it doesn't excel in anything other than having a high perception and scent. Even if the game did have a Level Adjustment system, I would qualify them as +0 and be forced to give them a few racial traits in order for them to be balanced with other playable races.