You have some crazy stuff going on here.
First, to my knowledge you cant board an aircraft with less than 6 months left on your passport. And if they do, you'll face a lot of problems at the immigration desk in Malaysia because the country has rules about that. You might be able to get in but then you wont be able to book a ticket out again. When you enter your passport info on an airline website they will block the booking if it has less than 6 months left.
Second, to answer you, you dont have to tell anyone you have sent your passport back for renewal, yes you can carry a copy. But.....thats not the law. A cop can look at your copy and then immediately ask you for the original and what are you going to do? If you say you sent it back and dont have it, that cop will force you to immigration at that moment and youre going to be detained.
Third, there is no such thing as an extension due to your passport being enroute somewhere. Any extension of anything for anything involves stamps into the actual passport. There is no possible way to get anything done on a photocopy of a passport.
I dont know where you are now but I would renew the passport before traveling and before coming here. Im american and our embassy would be the place to deal with getting it renewed so please ask your embassy how to do that if you are abroad now.
Since years, I carry my passport, not a copy, because Ive been asked for the original. Once, long ago as a tourist, I told a cop it was at my hotel and that cop followed me back to that hotel and made me produce it. Another time, under my work visa, i was stopped on my motorcycle. He didnt want the copy, and followed me back to my house for it. At the house, and there are now two cops, they began asking lots of questions. Who lives here? What are you doing here? We want to see the house and contents. Suddenly, a routine stupid little thing gets blown up like im a international celebrity man of mystery and everyone wants in on being nosy. Yeah, who is this foreigner? Whats he doing in there? Whos in there too? Lets all go see.
Malaysia has inconsistent rules and laws. Cops and other authorities do what they want to at the moment and they seldom error on the side of your convenience and happiness. They routinely overstep their authority and there is nothing you can do about it. In situations like I described, youd be ill-advised to argue with cops, like denying them entry into your hotel or house on the basis that they had no reasonable cause. THEY decide reasonable cause as they go. For this reason, you must always error on the side of doing too much, like carrying your real passport all the time and no matter how inconvenient it is, including your fear of risk of theft. Why? Because you never know how someone will handle a situation and your constant goal is to stay away from cops and govt office radars at all cost!