Do koalas eat nuts

No.

Koalas are known for feeding almost exclusively on eucalyptus leaves.

Besides gum leaves, they occasionally eat buds, flowers and bark of the particular species from which they get the leaves (which is not all eucalyptus species), while dirt also seems to supplement mineral deficiencies.

They do not eat nuts of any description - not even the "gumnuts" found on eucalyptus trees.