“the dollar’s decline is more because of extraordinarily low interest rates here rather than the increased money supply”
Say what? What do you think lowering the rate of interest does, besides increase the money (or, more precisely, credit) supply?
Keynes showed in the 30s that it is not always possible to increase the volume of loans merely through decreased interest rates. This is the “liquidity trap” wherein the extra money is not lent out because no one has the confidence to undertake loans.
But almost instantaneously the exchange rates will be impacted by the lowered interest rates. Since we have floating exchange rates now there is no true “devaluation” any more as was the case with fixed exchange rates based on a commodity standard (gold).
Also relevant in examining price changes is the Velocity of Circulation or the number of times a dollar is exchanged during a year. If V is extraordinarily low an increase in the money supply will not be reflected in price increases for a long time. If it is high then even small increases in M will produce a big impact on prices.