Considering a new card every year

We just enrolled our daughter in daycare. They auto draft from a card or bank each week. We already deposit money into our Ally savings account specifically for daycare. It draws 3.4% interest. Would it be worth each year getting a new cc with a 0% for so many months that has cash back. I’m thinking on the monthly statement pay the minimum and right before card drops 0% pay the full balance off with what has built up in the Ally account? Thinking we can earn interest throughout the year and cash back.