These eggs probably won't hatch into Facehuggers while you sleep. Probably.
Starfleet Regulations include one simple solution for dealing with the aftermath of a Tribble infestation
So you're on Fiji, shipwrecked, (near) comatose, and have access to fresh mango juice. You need a Mango Lassi. (Right after you have Kryten adjust the VR Simulator.)