Come on, the book itself is covered in fur... awesome.
Written by Margaret Wise Brown (Goodnight Moon, Runaway Bunny and many more), and illustrated by Garth Williams (also illustrated popular editions of Charlotte's Web, Bedtime for Francis, Little House on the Prairie)
Little Fur Family tells of a child's day in the woods. The day ends going 'up the wooden hill' to bed and with an impossible to sing bedtime song...
you try and find a tune that works.
A great site,
Vintage Books My Kid Loves, has a run down of more off-the beaten-path MWB offerings.
Further reading.