What does "this month" mean ?

If it's June,  "this month" means June.
So if today is June 25th, and you ask "which cows are due this month", you'll only see 5 days worth of cows listed.

If you want to see a month's (or a weeks) worth of cows listed,  use "due in the next 30 days", or "due in the next 7 days".
If it's currently June and you want to see cows due in July, you can use
   Which cows are due next month ?
or
  Which cows are due in July ?