If I transfer coins between two exchanges, is it important to get the time exactly right?

Could I just enter these as happening at 12am or does it need to be accurate down to the minute?

Internal transactions are not a big deal when it comes to date and time, as there is no tax implementation to those.
I would encourage you to be as close as possible though if you have a fee involved, so that the fee has the correct value at the time of transfer.