Can I target an already buffed Irelia Fervent with a Pit Rookie to get the +1 from Irelia's effect even though it does not get buffed again?

Yes, you can target an already buffed Irelia, Fervent with Pit Rookie's ability, and she will gain +1 Might from her own triggered ability.

Here is the breakdown of why this interaction works:

1. "Choosing" is sufficient: Irelia, Fervent's ability triggers "When you choose or ready me." According to RiftJudge FAQ #9143 and the rules governing targeting, the act of selecting a unit as the target for an ability—even if that ability fails to modify the unit (in this case, because Pit Rookie cannot apply a second buff)—counts as "choosing" that unit.
2. Pit Rookie's ability resolves: Even though Pit Rookie's instruction states it only buffs a unit if it doesn't already have one, the act of targeting her remains a valid choice. Pit Rookie's ability will still successfully target her, satisfy the "choose" condition for Irelia, Fervent, and trigger her +1 Might bonus.
3. Independence of effects: Because Irelia's triggered ability is separate from the effect of Pit Rookie, her ability will still be placed on the chain and resolve, granting her the +1 Might, even though Pit Rookie itself does not add a buff counter to her.

As noted in Rule 426.1.c, units that already have a buff counter can still be chosen for actions that buff units; they simply will not receive the buff counter itself. Because the action of targeting her is separate from the outcome of applying the buff, your intended play is legal and will trigger her bonus.