From my experience it doesn't matter how old your website is. Just make sure that you have enough good contents that are tied specifically to a niche. So, they can get appropriate ads for your site. I wrote, 'specifically tied to your niche' because google once complained about that to me. Don't get me wrong you can have as many as possible niche as you want but make sure you don't have like one article for each niche before applying. Also, like others suggested make sure you are already getting an ok traffic to your site.
But one advice I've for you, apply for adsense when you are already having a very nice traffic. This way you'll have less chance of getting banned.