Has the age at which menopause occurs changed throughout history?
Quick answer: Yes, but not in the last 150 years.

There seems to be no clear link between age at menarche and age at menopause (taken from [1]):


  While earlier studies were able to establish an association between
  early age of menarche and later menopause (Frisch 1978; 1987), more
  modern studies have not been able to confirm this effect (Whelan et
  al., 1990; van Noord et al., 1997).
  
  Aristotle's assessment was similar to those of Hippocrates and also
  Roman authors, so it seems that 2000 years ago most women entered the
  menopause in their early 40s. Mediaeval authors, however, gave the 50s
  as the age when menses ceased-much closer to the timing for twentieth
  century women.


Jean Ginsburg in [2] states (emphasis mine):


  In the past 100 years data from schoolchildren have shown a steady
  fall in the age at menarche in industrialised communities. Has
  there been a corresponding change in the age at the menopause?
  Unfortunately, reported surveys of the menopause have suffered from
  methodological defects. [...] 
  
  Nevertheless, those studies least subject to bias show a striking
  agreement that the median age at the menopause is currently around 50
  in Western industrialised societies. In Britain it is 50.78, in the
  United States 49.8 and in white South Africans 48.7 with little
  apparent change over the past century. In non-European women, however,
  the menopause seems to occur earlier-in South Africa and the United
  States black women have an earlier menopause than white women.


So, while early menarche is, apparently, irrelevant, age of onset of menopause has increased since antiquity but has remained relatively stable since the middle ages. Therefore, there have been no significant changes in the age of onset of menopause in the time frame you defined (150 years).

Finally, Bengtsson et al [3] state that:


  Our study has, thus, not supported the view that the menopausal age is
  rapidly changing.



C. Keck, Predictive Factors to Determine Age of Onset of Menopause, PAMJ
, 3, 2005
Ginsberg J. What determines the age at the menopause? BMJ. 1991 Jun
1;302:1288-9.
Calle Bengtsson, Olof Lindquist, Lasse Redvall, Is the menopausal age rapidly changing?, Maturitas, 1(3), February 1979, Pages 159-164