Until May 2010 the burqa does not appear to be a particular concern for Australians, with few searches of the term.
However since then it has become more topical, with some interest throughout 2011, then a sudden surge in September 2014 when the 'ban the burqa' movement began to receive significant political support and media coverage.
In contrast, terrorist was a term of interests to Australians in 2004 and particularly in the second half of 2005, with surging interest in July and November of that year. Following this, it settled down into a largely quiescent state, with only a small surge in November 2008 interrupting the mostly flat line.
This changed in August 2014, with a huge rise in searches for the term across Australia resulting in the highest level of searches for the term in the history of Google Trends in September this year.
The same trend can be seen for mentions of ISIS, which were flat until May 2014 and have rapidly escalated since. Early mentions of the term presumably relate to other uses of the term (such as the Egyptian god), with the sudden rise in searches only attributable to the rise of the Islamic State.
Searches for Islam and Muslim have also been rising this year after a long largely flat period. While these terms are the subject of many legitimate searches related to the culture and religion, the recent rise in searches does tend to suggest and correlate with the rise in searches for terror-related terms, indicating that people have linked the terms in some way, at least out of curiosity.
It's possible to compare and contrast these trends with global trends in Google Trends, per the chart below.
This chart provides evidence of growing global interest in terms such as Islam, Muslim and, particularly, ISIS. However it shows little international concern over the burqa or regarding terrorism.
This can be seen in detail when looking at individual countries.
For example while similar trends of increased interest in searching the term ISIS are visible for the US, UK, Canada, Sweden, Japan, Thailand and many others, only a relative few see the burqa as a rising source of concern and many also are not experiencing heightened searches for terms such as islam or muslim.
This may be coincidental, or may reflect political statements and media reports on these topics - a more detailed review of coverage would be needed to confirm direct links.
However given that researchers have found that Google Trends can provide an accurate view of community concerns regarding infectious diseases and product trends, I believe there's sound reasons to suppose a correlation between what leaders say and what people search for.