Advice needed for relocating to Singapore as contract worker

Your query is half informative and it's not clear whether you have family? If you have then they have to stay back in Malaysia as less than fixed basic $5000 salaried employees can't bring their family or spouse to Singapore.

If you are coming here as an unmarried person then you may stay in a rented room (a master room can cost you nearly $800 to $1100 depends on location), a common room can cost somewhere between $500 to $700.

With basic lifestyle you can save money of $2000 in each month, which is approx equivalent to your current drawn monthly salary MYR 6,500. So, not sure where and how you concluded by saying that your life style will be downloaded if you select a job here.

A general rule of thumb is that the number of MYR you need for a certain lifestyle in Malaysia is the number of S$ you need for that lifestyle in Singapore.
So if you can manage to live off MYR2000 in Malaysia, you need S$2000 for the same in Singapore and can save the other S$2000 of your salary.
But certainly the chances to spend more (and the temptation) are greater in Singapore!

You can always elect to maintain a residence in Johor, while commuting daily.