that's not the right answer.
since you are both the child's parents and live together the IRS has the following tie-breaking rule on who can claim. based on what you provided it's the parent with the highest Adjusted Gross Income.
IRC 152(c)(4)(B) More than 1 parent claiming qualifying child
If the parents claiming any qualifying child do not file a joint return together, such child shall be treated as the qualifying child of—
(i)the parent with whom the child resided for the longest period of time during the taxable year, or
(ii)if the child resides with both parents for the same amount of time during such taxable year, the parent with the highest adjusted gross income.
