Check out :
http://www.federalreserve.gov/releases/h6/current/
Actually, M1 has been relatively constant for the last two years. M2 has come up a little over ten percent total in that time period. Hardly an "unprecedented" rate, and due more to an improving economy than anything else. Yes, the American economy is rather healthy, despite what CNN tells you. Inflation is fairly low, which certainly wouldn't be the case if the Fed printing presses were out of control. The high price of oil is largely due to a sharp increase in demand (mainly China, or so I'm told).
I can't comment on Dubai's inflation rate (I've spent a total of three weeks there this year), but I'll bet a drop in the dollar has relatively little to do with it. Eventually the dollar will reverse direction. Prices in Dubai, it seems, won't.