Some background:
I don't want to reject the extension before I found something else. My contract doesn't specify how much notice I have to go. What's the best strategy to postpone giving them an answer for as long as possible? What are the usual practices in such situations?
A couple of suggestions based on the fact that you want to move on;
Find out your notice period (if applicable). Agree a fixed day to provide your answer, sooner the better.
Reasoning - secure where you are before considering moving on somewhere else.
Ultimately there is no reason why you cannot find another contract when in employment, simply have phone interviews, interviews at the end of the day or beginning instead. This is a commonly done thing nowadays and can in fact impress the future employer knowing that you seem to take your commitment to your current role seriously.
The sooner you get a new role the sooner you are out of where you don't want to be.
