IMHO :

The US Dollar has had (and still has) the enormous advantage of being the world reserve currency.

That unique attribute permits the FED to export and distribute its inflation to other nations.
Or described in other words forces other nations to devalue their domestic currencies in pair with the US Dollar in order to remain competivite in world trade according to their respective import/export requirements and desired trade balances.

Since inflation is already running relatively hot since many years, this allows for a unique cushioning effect, as the inflationary developments can be distributed worldwide PLUS they seep through very long channels before becoming effective. Where needed, all western-oriented central banks worldwide act in perfect harmony to ensure the distribution is averaged amongst their respective nations.

In comparison, any other nation inflating its domestic currency at the rates i.e. the FED does it , would eventually suffer the same consequences - BUT they'd arrive far quicker and in a far more linear fashion. This effect can (and occasionally is) only be countered by individual "friendly" central banks increasing their reserves of that currency in their foreign currency reserves basket in order to stabilize that affected currency in question.

Other than that, in today's bizarro FX markets, having the right "talking heads" issuing the right prepared statements as a promise for future action often is enough - even if they're empty promises and based on nothing but fairytales and unicorns.
(i.e. ECB's Mario "Goldman Sachs" Draghi stating to "do whatever it takes to save the Euro" or Ben "Shalom" Bernanke stating "no bubble there" or "sees no significant risk of inflation")

In short :
It's already developing but it's highly assymmetric and delayed by many factors - however, it is still unavoidable if the present course is kept.
However, the entire above mechanisms will be bypassed and inflation kicked into high gear as soon as the US Petrodollar monopoly is abandoned by sufficient countries.
And this is exactly what we're seeing since about 2 years now.
(previous attempts of bypassing the US Dollar in international trades so far resulted in governments being toppled and/or nations being destroyed/invaded by US forces to install a Dollar-friendly muppet regime - but now it's China and Russia that openly challenge the Petrodollar, which is a whole new playing field).

Historically, nations enjoying the status of issuing the world's reserve currency became great and wealthy empires - however this luxury never lasts forever and all of these empires imploded more or less after losing this status. When the day of reckoning comes, I assume the US is fully prepared for it (just look at its military, foreign/domestic policies and intense foreign/domestic preparations. This is what a country looks like that is preparing domestically for a complete loss of prevailing social order and ready to commit to a very large war abroad)