It's true that financial assets compete with each other for investors. So when the Fed reduces the yield on Treasurys or MBS, the marginal investor will rotate to a riskier asset. This will create a chain reaction that eventually raises equity prices. However, it's not the case that earnings yield (Earnings/price or the inverse of P/E) is going to be equivalent to the interest rate on Treasurys (T-bills). Typically the way that investors think about it is earnings yield = Treasury rate + equity risk premium. So at an equity risk premium of 5%, even a Treasury rate of 0% would result in an earnings yield of 5% or P/E of 20, not infinity. This isn't too far from the market multiple of the S&P 500 right now. (The historical average ERP over the past century has been 4.2%.) So the market multiple implies that the overall market is not in a bubble, but that doesn't eliminate the possibility that some sectors are in a bubble.
The Fed's influence on the market goes beyond their impact on interest rates. One reason for the sharp rise in markets is that investors are fearful of inflation. Although CPI inflation has remained low, investors would rather hold scarce assets such as equities and real estate than a rapidly diminishing percentage of the money supply (i.e., cash) that results from money "printing". While money creation is nothing new, and in a sense, unconventional money creation is not that different than conventional easing, the sheer scale of our current monetary policy is unprecedented. This lack of precedent creates a high degree of uncertainty in the ultimate outcome.
The final reason for the strength of the markets is a widespread belief that the "Fed put" is back. It is almost universally believed that the Fed has taken on a third, unstated mandate of stable and rising equity markets, by easing and talking the market up when it declines. I don’t know to what extent this is true, but the mere notion has created a hidden source of instability in the market by giving investors unusual confidence. While there is no reason to believe that markets will crash, it's also not out of the question.
The Fed has announced that it will "taper" QE purchases from $75 billion / month to $55 billion / month. At the current rate of taper, QE purchases could reach zero by the end of the year. One key question for investors is whether this may reverse any of the three dynamics listed above.