She won't "die", she will just go back to her home planet. Wait until tomorrow and switch the time to 11:59 PM and you should see your tama flying away in 1 minute.
At mid-night of the second day* the parent will wake up and turn on the lights, but the baby will remain sleeping in bed. The parent will just stand there for about 3 minutes, then jump up and disappear off the screen. (The lights will turn off again, automatically.) When the baby wakes up in the morning, s/he will be alone.
(* example: if your Tamagotchi character mated and had a baby at 10:30 AM Thursday, then the parent will leave the baby at midnight as Friday becomes Saturday.)