Lay out your felt on a large table, or well-swept floor. Measure around the waist of the person who will be wearing the skirt. Fold the felt in half both ways to locate the center. Measure down from this center point along both folds extending from the center and mark the felt at 1/4 the distance around the waist of the wearer, plus 1/2 inch.
Use a french curve ruler, available at craft and hobby stores, to draw a curve across the piece from one mark to the other. Measure down from the first mark along each edge, the length you want the skirt to be from the waist down to the hem. Mark each edge and use the french curve to draw a line between them.
Cut along both lines, with the felt still folded with heavy fabric scissors. Unfold the felt to reveal a large circle, with a circular hole a little larger than the wearer's waist. Fit the skirt around the wearer and pull the waist tight. Mark the felt where the pieces overlap. Attach a piece of adhesive hook and loop fastening tape in the waist, the hook on the inside piece of the overlap, the eye on the outside.
Measure down the line of the overlap and add hook and loop tape every 6 inches to hold the skirt closed.
Purchase a prefab felt poodle from a hobby store, or find a poodle skirt image and draw your own on white or pink felt. Use fabric glue to glue the poodle on the front of the skirt to one side, three or four inches up from the hem. Glue on looped yarn the color of the poodle for its fur.