I want to power up an Arduino toy car with this UPS but I am not sure if I can charge this UPS with a 9 Volt 0.6 Ampere power adapter.
The miniUPS clearly states that it takes an input of 12 V and a current greater than 1 A.
The voltage of the input is the most important. Using a 9 V supply will probably not supply sufficient voltage to charge the miniUPS, which is 12 V - so there is a deficit of 3V.
The current of the power supply isn't such a major issue: if the current is lower than specified to be required, then charging will probably just take (much) longer.
That said, plug it in and see if it charges. It probably will not, but try it and see.