That's not what's needed for Peak Oil. Peak Oil means even with higher demand, as we have now, there won't be more Oil on the market. And that's exactly what happens since around 2005/2006: the absolute amount of oil extracted and sold sinks slowly every year, while before that it increased always except in times of severe crisis, economic or price hikes (1970s).
And why don't we have more oil on the market? Please ask yourself this question honestly. You seem to jump to the conclusion that the *ONLY* reason we don't have more on the market is because there just isn't any more to produce. That is not true.
1) China's and India's economies have been expanding at an insane pace in the last 10 years. More people in those countries drive cars now than every before. The demand has continually been increasing.
2) Developed nations (most notably the U.S. and Canada) have politically decided that oil is "dirty" and entire industries have been prevented from expanded production of oil in these 2 nations (which have vast tracks of land, full of oil), this is to say nothing of the rest of the world, which seemed quite content to just let the monopoly OPEC exist and just deal with them.
World oil isn't running out, our demand is not out-stripping our potential supply, it's just monopolized.