the vac idea seems a bit worrying to me I would accidently vac it up.
I would try:
Darken the room and use a strong light, torch or spotlight to slowly scan the floor to see if the light hits the diamond and shows up
Use masking tape or cellotape wrapped around your hand, press it down to pick up loose 'stuff on the carpet.
Check the bottom treads of shoes that may have been walked on the carpet.
Check inside stuff eg random stuff round the room it may have fallen in..boxes? Even inside your clothes - your bra you socks etc
Have you got anything that could magnify the carpet some strong reading glasses you can scan the carpet with.
Re trace you steps and look where you may have walked the diamond earlier.
Look down the edge of the carpet/skirting board, around door frames and the strip of metal across the middle of the doorway - dont know what you call it.