A book chapter by Francesco Billari says,
In 1980, in most countries [the report is on Europe], first marriage was experienced on average before age 25 for women: only a few exceptions existed. This pattern completely changed in the next 20 years: by 2000, in only a small minority of countries is the mean age at first marriage lower than 25.
...In 1980, only a few cases of ‘low’ [between 1.3 and 1.5 children per woman] fertility levels were recorded (for the former Federal Republic of Germany, Luxembourg and San Marino). By 2000, 11 countries have ‘lowest low’ fertility [below 1.5 children per woman] and 11 have ‘very low’ (but not lowest low fertility). At the beginning of the new millennium, very low fertility is pervading the UNECE area, and lowest low fertility is present in a substantial group of countries. In fact, very few countries, which belong to quite different regions, have fertility above two children per woman (Iceland, Israel, Kyrgyzistan, Turkey, the United States and Uzbekistan).
The population halving time for a country with a fertility rate of 1.5 is 65 years. For a fertility rate of 1.3, the halving time is 32 years.
The table of contents for the full book can be found here.
Small correction: According to the document you linked, the halving time of 32 years corresponds to a fertility rate of 1.1. For 1.3, the halving time is 44 years.
Point still remains, and fascinating article.
I believe that "problems" like this correct themselves. I predict that Italy and Japan will have a fertility above 1.8 by 2050.
Why should the problem be necessarily self-correcting on any time scale but the very long run? As seniors become a larger fraction of the population, the tax burden they represent to working would-be child-rearers grows, and so the means of families to have more children shrinks.
At least one demographer has hypothesized that there is a low-fertility trap. At least to date, no country has come back from below TFR = 1.5.
http://fistfulofeuros.net/archives/001748.php
It would be interesting to know what happened in other historical episodes of population decline. For example, Greece between 0 to 400 AD and Rome a little later.