Why should it be ? If it was a protracted process (or one that changed - "I started killing two rabbits but then changed my mind/decided to kill fifty/etc.) then this is perfectly good English ...
And would "I started to kill two rabbits" be different in Romanian? (This English sentence might mean that I didn't decided not to kill them after all)
Well something definitely has to be changed, but considering the fact that it's an exercise where the Romanian sentence is given, and you have to provide the English translation, I suppose it makes most sense to rectify the English sentence.
And in case you missed it:
- Am început omorând doi iepuri. = I started by killing two rabbits.
- Am început să omor doi iepuri. = I started killing two rabbits.
All sentences for this exercise en-ro and ro-en can be used , no one is wrong