Here is an old-fashion push toy.
The original toy had a simple wooden ball on the end of the push rod but a 'T' shaped handle affords better control..

Penguin Push Toy. Right-Click on the picture for the drawing. The drawings are full scale drawings. These plans are created in Adobe Acrobat Reader (.pdf) files.

Detailed Instructions
*********** WARNING***********
Read my page on safety before building this item.

Materials needed:
Any choice of woods will work. I used common dowels and pine planking.
Be sure to use ONLY child safe paints on these iems.

Construction:
This is a pretty simple project. Simply use the drawing as a guide (or click above for and Adobe pdf file). Cut out the body and the wheels then locate and drill the holes for the push rod, the wings, and the wheel axle. Cut the notch in the wheels for the feet. Cut the wings and feet from a heavy duty automobile or truck inner tube. Now, sand all rough edges, paint the wood (always use child safe paint), glue the wheels on, glue the feet into the wheels, glue/stick a set of large 'google' eyes on, and pull the wings through the body hole. Push the push rod (dowel) into one of the holes but do not glue it. The holes serve as a height adjustment.