I found out that IE does not take the next element after an LI,it directly picks the next element of same node type,whereas FF properly checks the next element after LI.
Once again here,IE sucks...
So,I modified my html page so as to contain the <P> inside <LI> as follows:
<li><a href="#" id="Q1" onClick="Toggle(event)">Question 1</a>
<p>Here is your answer</p></li>
<li><a href="#" id="Q2">Question 2</a>
<p>Here is your answer.</p></li>
..and then I used the lastChild property instead of nextSibling in the JS code as follows:
This solved my problem as both IE and FF returned the <P> tag for lastChild.
Thanks all for your time.