Yes eucalyptus oil will kill fleas on your pet and on bedding and anything else.
You can take a spray bottle and fill it with water and then add 5 to 6 drops of eucalyptus oil to the water and then mix it up by shaking the spray bottle.
Then spray the solution onto the bedding, toys or anything else the fleas may be on and you can also spray it on furniture where the fleas are too.
The eucalyptus oil will not only kill the fleas but the smell of the eucalyptus oil will actually repel any other fleas from the area.
You can also add a drop of eucalyptus oil to your dogs neck or collar to kill and repel fleas on your dog.
Or you can apply a few drops of the eucalyptus oil to your dogs back to kill off any fleas and repel them from your dog.
You should also bathe your dog in flea shampoo or give the dog a flea dip every once in awhile to keep the fleas at bay.