Well, it is probably a scam and I will go over that in a moment. But here is a link from the Malaysian government and you see that there is no set fee, just a maximum:http://www.imi.gov.my/index.php/en/main-services/enforcement/overstayed
So it looks like the maximum is a little over $3000.
Unfortunately, I still believe it is a scam. Believe me that I understand especially when one's feelings are involved and one is a good person and wants to help. I almost fell into something similar myself.
Normally the scam starts with trying to establish a romantic relationship, perhaps just a friendship at first. They also may claim to be a citizen of the UK or US or wherever so that you would not suspect they have any ulterior motive. They pull at your heartstrings by telling stories of hardship or tragedy that they have suffered in their life. At some point they want to come visit. They may ask you to send money for a passport and/or plane ticket. They may tell you that they have money, perhaps even that they are wealthy, but their money is tied up or something like that, perhaps they tie it into a tragedy or something. Then the next step is when they supposedly have the passport and plane ticket, they suddenly come up with this Basic Travel Allowance or (BTA) which is supposedly to show authorities that they have enough money to fund their trip. This is a lie. There is no such thing. Or as in this case, they use an already existing and verifyable law to back up their scam. They ask you to send that money. This is just another method to steal money from you. Then the next part of the scam would be when they are supposed to arrive. You wait for them at the airport and they never show up. A few days go by, you get extremely worried, none of your methods of communication work, and then suddenly a "friend" or "relative" of the scammer contacts you to let you know that she has been detained/arrested by authorities for carrying something illegal, I have heard of unregistered gold and they say it would have been a gift for you (perhaps to pay you back for the money you sent). The friend or relative of the scammer then asks for you to send money to bribe or pay fines in order to have the scammer released. From there, I have not heard of how else they are able to get money out of people. Of course there are variations to the scheme, but that's pretty much how it goes.
Here is a link that you can go to for more information:
http://ghana.usembassy.gov/romance_scam.html (yes, it is a link from the U.S. Embassy in Ghana, but it applies to all different countries and I have seen this scam come from Russia, the Ukraine, Nigeria, many other countries, and yes, even Malaysia).
And here is another link from the government of Ghana:
Please let me know if you have additional questions and please do not forget to rate my service to you (not the state of the law) as that is the only way that I can get credit for my assistance to you. Even after you rate the service, I can still answer additional questions for you without additional charge. If you do rate me positively, a bonus is always appreciated. If you would like to request me in the future, just go to http://www.justanswer.com/law/expert-guillermosenmartin/ and make sure you type: FOR GUILLERMO on the subject line. Thank you!