It's already in the game, you can just ask to be kicked. You don't get a penalty from that anyway. You can't be matched with that party if you re-queue but who cares. They probably have a replacement by the time you get back anyway.

If it is something quick like you need 2 minutes to untangle a kitten from some yarn just tell your party and they will probably wait. If its something more serious like your kid dumped the contents of the refrigerator on the floor then just leave and take the penalty since it's gonna take you 30 mins to clean that up anyway.

Most RL things tend to either fall into the 1-5 minutes where the party will wait or kick your or 25-??? minutes where you won't notice your penalty anyway.

Most of all, just communicate with your party. Tell them your cat is on fire and they can decide to wait 3 minutes or kick you.