YOU SAID:

I will go eating with my cat this afternoon

INTO JAPANESE

私は今日の午後私の猫を食べて行く

BACK INTO ENGLISH

I go eat my cat this afternoon

INTO JAPANESE

今日の午後私の猫を食べに行く

BACK INTO ENGLISH

Going to eat my cat this afternoon

INTO JAPANESE

今日の午後私の猫を食べに行く

BACK INTO ENGLISH

Going to eat my cat this afternoon