Oh u just started out...it's very good that u started to have financial consciousness at such young age.
Yes, it'd be a good idea; every few months u go place a RM1K FD. Don't put long-term, 2-month tenure (for 1-month tenure, min. amount is RM5K) would do since it's just an emergency reserve, u wouldn't want to place a 12-months FD and then having to withdraw it at 11th month and lose 1/2 of the contracted rate.
Focus on building sufficient emergency reserve first, then only think about investments.
Over long term (10 years and above), a well-managed fund can quite safely outperform your housing loan interest rate. As I've said, u have time on your side, you're young, u can withstand the temporary shocks that the market might present you.
If you don't wanna worry too much/spend too much time learning and monitoring, I'd suggest that you pick 1 good "balanced" fund and just do monthly Dollar Cost Average on it (e.g. invest RM200 into it no matter what happens), over time u should see the fruits.
U can learn about unit trusts from Public Mutual thread, Fund Investment Corner and Fundsupermart.com threads here.

In this case, in order to build up my emergency fund quicker, would it be wise for me to allocate the extra money into my emergency fund until it reach a specified target (lets say RM10k) before I invest it into unit trust? Or should I just slowly build up the emergency fund by RM300 per month and invest the remaining unit trust?
Thanks for the advice, I will learn more bout unit trust from the site you suggested