I know my battery should be replaced, but is that all of the problem? (Update)
You can leave your battery unchanged as long as you want, even it is not recommended by the operating system (i.e. Apple). 

From my own experience (2011 MacBook Air with 1178 load cycles), the battery performance will just degrade more.

It may be be months away, but at one point the battery will be so weak that an unplugged Mac will not go to sleep when the battery is empty, but just shut down. Trust me, you will notice.

An Apple Store employee told me that battery replacements can often be done while you wait, or within a few hours if you make a Genius Bar appointment rather early in the morning.

Good luck!