Bitcoin works regardless of the price. There is nothing to worry about, even if it drops below $1.
This is incorrect. The concept "works" but for practical purposes Bitcoin does not.
A) Bitcoin, with its existing 1MB limit on blocks, is limited to 7tx/sec (according to Bitcoin Wiki). Bitcoin's market cap and average BTC per address directly affect how much wealth can be transacted through Bitcoin in any given period of time. Therefore it directly affects how well the Bitcoin system can function as a payment processor.
B) Bitcoin's functions are very much price dependent. For instance, a multi-billion dollar corporation would not view Bitcoin as a suitable substitute for wire transfers if the market cannot absorb the entry and exit of a corresponding amount of wealth without vast price fluctuations.
There's a feedback mechanism here that too many people are too willing to ignore. These are some of the basic reasons that people expect Bitcoin's price to grow exponentially at some point, and not in the sense of a bubble. Needless to say, Bitcoin may currently be overvalued and continue to crash. However I believe it is too soon for a serious crash and would expect such a crash to occur when the FED (US/Japan in particular) begin tightening their monetary policy.
Therefore I would expect Bitcoin exchange rates to exhibit strong momentum around certain price points, depending on the economy's stage of growth. A decrease begets a decrease.