Do you think Chloe would try to eat a rug like this? Flor tiles are like finished squares of carpet that stick to the floor (but are removable and washable). This could be a nice option for a long rug at the foot of the bed. Not as thrifty as the IKEA options, though.
FLOR STAMPEDE carpet tiles from CB2 / $14.95 (x10) = $149.50
I doubt she would try. I think the chewing thing is just a little bit of the puppy left in her. As long as there are no threads or tufts sticking out of something she is usually not tempted.