Introducing my girlfriend - advice needed

Been dating Sarah for 8 months now and I have my kids (11, 14, 16) this coming weekend. My ex doesn't know about Sarah yet and honestly I've been hesitant to introduce her because my oldest has been through two of my previous relationships and I don't want him rolling his eyes at me again. But Sarah's wondering when she'll meet them and it's getting awkward. How long did you all wait? Is 8 months reasonable or is that too fast? I feel like at 11 years old the youngest doesn't care as much but my 16yo will definitely judge me lol