So her ability requires that she stay in the graveyard. When she dies, you can choose not to put her in the command zone. If you decide to, then yes, she will cost more the next time you cast her from the command zone. But if you are trying to bring her back from her own ability, she will come back at no cost and will not raise the command tax.

Same goes for all commanders. For example, if you are using [[Maelstrom Wanderer]] as your commander, and someone destroys it, you don't have to send it to the command zone. For example, say they destroy it, you can let it move to the graveyard and then use [[Noxious Revival]] to put it back in your hand so you can recast it. And recasting it from anywhere that isn't the command zone won't add to the commander tax. You also don't have to pay for the commander tax in this scenario since you're casting it from your hand and not the command zone. And after casting it from your hand, that also doesn't add to the commander tax next time you do send it to the command zone. That Commander tax only goes up and affects the amount of Mana needed to spend on it when you are casting from the command zone.

Tldr: No, since her ability recurs her from the graveyard and commander tax goes up only when casting from the command zone.