The online version of the CIA World Fact Book can list all countries by fertility rate.
It's not completely clear what you're asking, but I believe you're looking for a 'developed' country with a fertility rate higher than ~2.1 - 2.3. If that is your question, I offer the following countries from the World Fact Book list that are generally considered to be 'developed':
- Argentina 2.31
- United Arab Emirates 2.40
- World (for reference) 2.46
- Kuwait 2.64
- Israel 2.70
The extreme low fertility rates of Hong Kong (1.07) and Singapore (1.11) do not prevent them from experiencing population growth, rather than steady-state or decline, because there is sufficient immigration. Hong Kong has a population growth rate of 0.448%--not huge, but it is still positive. Singapore's growth rate is 0.817%.
For reference, here are the growth rates for the counties listed earlier:
- Argentina 1.02%
- United Arab Emirates 3.28%
- World 1.09%
- Kuwait 1.99%
- Israel 1.58%
Most developed countries are at no risk for decline because there is enough immigration to offset their lower fertility rates. Two notable exception are Germany, with a growth rate of -0.21%, and Japan, with a growth rate of -0.28%.
(2011-03-25) In response to questions from the OP:
The grammar in the initial question,
Does women working outside the home automatically drive below the replacement threshold?
has a fair level of ambiguity. Based on the paragraph that followed, I interpreted that question to be asking if there are any 'developed' countries where the fertility rate is higher than the assumed steady-state value of 2.1 for 'developed', 2.33 for world average, and higher for undeveloped, countries. This is also what the ambiguously worded title question asks if you assume a direct correlation between 'developed' and 'women working':
Is the fertility rate of women who work over 2 children anywhere in the world?
In my original answer (see response above the edit line), attempted to provide evidence that there are some 'developed' countries where the fertility rate is higher than the assumed steady-state values that had been provided.
If I reinterpret the question asked in the body of the question (see first quote) as "Does having more women working outside of their own household cause lower fertility rates?" then I must answer: There is insufficient evidence to prove a cause/effect relationship between 'working women' and low fertility rates.
While there is evidence to show a correlation between the two (higher 'development' and lower fertility rate), it does not show which, if any, causes the other. You could just as easily claim that lower fertility rates cause a nation to become more developed and theorize various reasons for this phenomenon, such as: With lower fertility rates, there is less competition for food resources which allows more time to develop technology. There is further 'proof' of this in nature, where animals with lower fertility rates, such as elephants (5-10 per lifetime) or dolphins (~16 per lifetime), are much more highly developed than animals with high fertility rates, such as rabbits (10-30 per year) or fruit flies (up to 900 per lifetime).
Reproductive strategies vary between different animals, and can vary within different populations of the same animal (as evidenced by the different fertility rates of humans in different countries.) Animals with fewer offspring can afford to spend more time developing each one so that they have a higher chance of survival into their reproductive period, and that (high survival rate) is the essence of what it means to be 'developed'.
If this additional response still doesn't answer your question, please consider revising your question using proper English grammar.