Or, if each page has a whole month:
You probably already have a grid built for each month. It should be 6 weeks of 7 days each to fit all possible date combinations.
You probably also already have boxes to contain the dates, one for each day of the month. Make sure there's one for every day on the grid, even for days that may not have a date in that particular month.
Starting with the top left box, link all those boxes together in order (option-click the linking tool so it sticks, then click on each successive box through the whole month). You'll see arrows connecting all the boxes together (you'll want your guides turned on for this part).
Enter "1" in the first text box, then hit the "Enter" key on the numeric keypad (not the "Return" key) to move to the next empty box. Enter the remaining numbers 2-31, each in its own successive box.
Place your cursor before the "1" in the first box. Hit the "Enter" key until the 1 is on the correct day. This will move all the other numbers forward as well.
Next year, if you need to move the "1" backwards, place your cursor before the "1" and hit the "Delete" key until the 1 is on the correct day.
Once you've built that first month and it's working like it's supposed to, you could group the whole page, then copy and paste it onto the other 11 month pages. Or, you could group just the newly linked date text boxes, then copy and paste that into the remaining months. So you really only have to build the "linked text boxes" part once.
This would also work if all your months are on a single page, like a poster. Just build one month, then copy and paste it for the remaining months.