What components I need for a small GPS tracker
You have two options. Option 1. Buy a ready made pet tracking device from online market e.g (https://www.aliexpress.com/item/Pets-Smart-Mini-GPS-Tracker-Anti-Lost-Waterproof-Bluetooth-Tracer-For-Pet-Dog-Cat-Keys-Wallet/32887784462.html?spm=2114.search0104.3.1.26793604pFMLma&amp;ws_ab_test=searchweb0_0,searchweb201602_3_10065_10068_319_10059_10884_317_10887_10696_321_322_10084_453_10083_454_10103_10618_10307_537_536,searchweb201603_52,ppcSwitch_0&amp;algo_expid=09c58262-a0e7-4205-8fba-cd8265c15b3e-0&amp;algo_pvid=09c58262-a0e7-4205-8fba-cd8265c15b3e). Then you can download the app and start tracking movement.

Option 2: The other alternative is to build one from scratch by purchasing all the necessary components. This is option is most appropriate for students. You can check this page for more https://electronicsforu.com/electronics-projects/hardware-diy/gsm-gps-based-vehicle-tracking-system. However, you may not be able to achieve the small size as you wanted but you should have something close to it if you carefully select your components.