Your birthday milestone is about the evening, not the math behind the reservation. Booking a weeknight can cut venue fees significantly, which leaves more room for a better menu or extra guests.
You want to lock in your date at least three months out to secure the space. Once you have the final quote, you can spread the cost over the coming months to keep your monthly cash flow steady.
The 0% intro APR on this card is a tool to manage your cash flow, not a discount on the price. If you have a balance left over after the 15-month window ends, you will start paying interest on whatever remains.