Possible Clues:

• Ann or Andy
• Cloth plaything
• Cloth toy
• Hit for Aerosmith and The 4 Seasons (different songs, though)
• Docile cat breed developed in California in the 1960s
• Dollar surprisingly secures good toy
• Floppy figure
• Toy with Page 3 cutie?
• 1964 Four Seasons hit
• 'Small cloth replica of a person (3,4)'