Can I say just "short of time" instead of "short amount of time"?
"Short of time" is not really a phrase and does not have the same meaning as "a short amount of time" in this case, so it would be incorrect to use "short of time" here. If you drop "of" and just say "short time" this is grammatically correct and could be replaced here, however it is less common than "short amount of time." The word "amount" here really emphasizes that the the time was short, and so it is important to use in this context. Ex: She's grown a lot in a very short time. Ex: He ate his meal in a very short amount of time.