Upvote:2
Spirit Airlines charges for advance seat assignments, so yes you need to pay if you want to request seating in advance. Just because you have a child traveling with you is not grounds for them to waive that fee.
That said, in most likelihood, the counter agent checking you in or the automatic assignment algorithm will take into consideration that you are traveling with someone on a child's fare (assuming you bought a child specific airfare and not a standard ticket) and assign adjacent seats if possible.
But if you wanted a guarantee of seats together, you need to pay the fee.