It is quite difficult to define exactly the period of time that would be enough to go to live trading. It depends on number of trades and also on your understanding of the market. The main idea is that you should be able to execute trades without serious mistakes like breaching the rules, prescribed by your trading system.
Despite all doubts, demo account is very important. Almost all professional traders started their path from demo trading, and even now they use demo trading to get familiar with new strategies. It is very usefull tool for many reasons. First of all, trading on demo you can practice such skills like placing orders or making other operations. For sure, while trading on demo you will alway remember that these money are not real, so there would be no psychological pressure or such feelings like fear or gread. At the same time, if the trader acts strictly in accordance with the rules of his trading system the impact of such feelings would be reduced even on real account. That is why demo trading is useful even if it doesn`t cover psychological aspects.
There could be other possible solution - trading on cent account, that is something between demo and real accounts. From the one point of view, funds on cent account are real, so the feelings during trading would be close to reality. But from the other side, both wins and losses on cent account are too small to inluence your financial standing, so this tools if for education, not for earning money.