Final Fantasy IX is not a very hard game, you should be able to complete the game fairly easily on low levels. During my first few playthroughs I used to level up as early and as much as I could, but I always found the game too easy. Now, I seldom make a habit of levelling up more than the ordinary, although I don't run from battles in order to avoid levelling up.

But yeah, levels shouldn't be that much of a problem, as long as you have good equipment and abilities.