A city shall have power to levy an annual license tax on the privilege of keeping any domestic animal, including dogs and cats, within the city. This section shall not limit the city’s authority to enact ordinances under N.C. Gen. Stat. § 160A-186 (R.C., c. 111, s. 13; 1862, c. 51; Code, s. 3800; Rev., s. 2924; C.S., s. 2677; 1949, c. 933; 1971, c. 698, s. 1.)