First, take a look a the following:

http://en.wikipedia.org/wiki/Key_money

Key money is used differently in different parts of the world and sometimes means money paid to an existing tenant who assigns a lease to a new tenant where the rent is below market. In other parts of the world it is used synonymously with security deposits.

In the United States and the United Kingdom, it is illegal for landlords to require key money. . . . .

In France it is the norm that a tenant that assigns a lease is paid an amount for a lease that is below market. . . .

It is also common in many countries to require 'Key Money' in the form of a security deposit. . . .

In Japan, however, key money is non-refundable and often amounts to several times the monthly rent, totaling as much as six months or more. . . .

In Korea, the key money system (Jeonse, as opposed to monthly rent or Wolse) requires the lessee to make a deposit of about 60%~70% of the housing price. . . .

The above-excerpted Wikipedia article contains some additional information that I left out.

The point is that since there is no single meaning for the term, one should not expect to have a univocal term in Arabic for it. It all depends on how it is used.

The meaning you state in your explanation is unique. It is simply means the rent paid in advance. For that, I would suggest إيجار مقدم

For "key money" in general, the expresions
خلو أو خلو رجل
are not bad at all, so long as the context supports it.

For a more inclusive term, one would have to basically invent one. I would suggest
مهر الشقة أو صداق الشقة