Do I have to protect the CD4013 outputs from short circuits?
datasheet says


  Device dissipation per output transistor: 100 mW


There's your output current limit. if it's running from a 5V supply if you short it to ground and more than 20mA flows you've exceeded that. At 5V this seems unlikely to be possible, the outputs just can't produce that much current.

However at 15V Vcc it's only 6.7mA to damage it - and that's probably attainable with real-world parts.