I'd be very wary of that strategy. Having read up on this recently, the consensus is that during the current credit-crunch crisis, there has been a bit of a 'flight to quality' to the US dollar, while markets settle down. The reason for this is that it is the most traded currency, and thus represents stability and liquidity, which is what investors look for in times of crises.
Underlying fundamentals are not so rosy however, and in the Wall Street Journal today, they predict that once the current environment settles down, continued weakness in the dollar is to be expected.
In addition, it appears the actions of the ECB at the end of last week has had the desired effect on the credit markets, thus it is still a likelihood that there is at least one more interest rate rise in Europe this year, even if it is deferred until after September. This will lend further support to the Euro versus the dollar, so I think to be honest you would be very unwise pursuing the strategy outlined.
Perhaps a better risk might be to buy into the stock market now, as given the recent falls, there could be a significant bounce once confidence is restored, as the current indicators seem to suggest