'07 Gear selection problems

Please, our 2007 Corolla finds it hard to select reverse gear promptly these days; the Reverse Gear idles and fails to select automatically. In addition, the Drive Gear doesn't select on time, it delays for few seconds, then jerks forward when it does select. What could be wrong? Is it the timing belt that needs changing? The mileage is 212,989km. Thank you.