Enzo from ReBoot is one of the better depictions of this. Part of the reason is that while he frequently gets kidnapped and bites off more then he can chew, the awesomeness of The Hero Bob is seen through his eyes. And Character Development has him rising up to the occasion to be a hero himself when Bob is stranded in the web.
Gorgonzola from Chowder. Gorgonzola has a Freudian Excuse. Namely, he's stuck learning a job he hates (carrying a candle on his head and not allowing it to go out), while his peers all seem happy with the paths their lives have set before them. Not really a surprise, then, that he's so intent on making their lives as hard as possible. He's not so much 'bratty' as he is just a jerkass.
Ash in Fantastic Mr. Fox is actually older than his unbearably perfect cousin, Kristofferson, but he otherwise fits the character trope with his resentful ill temper. However, he dramatically matures in the story and becomes a nice kit at the end.
Imp from She Ra Princess Of Power is another good example from Filmation. While his age is never established, Imp has all the earmarks of this characterization, right down to throwing childish tantrums when he doesn't get his way.
Codename: Kids Next Door contained two examples; Numbuh Two's little brother, Tommy, and Numbuh Three's little sister, Mushi, but it's not until the episode "Operation: C.L.U.E." that Mushi totally becomes a full-on emphasis of Bratty Half-Pint when she was revealed as the culprit who stabbed Numbuh Three's rainbow monkey in the back.
Pretty much the entire KND ensemble is this to some degree, especially in early episodes, where the team were more a defiant bunch of rebels to adults than outright heroic.
D.W. from Arthur is a classic example of this trope. So much so that many fans cheered when Arthur finally punched her in one episode, which was treated as a What the Hell, Hero? moment in the show. To be fair, she ended up breaking Arthur's model plane —a project he spent the entire week working on— after he told her multiple times not to touch it.
Bart from The Simpsons. If you get his name as an anagram for "brat", he's quite the example. Lisa also displays some shade of being a brat due to her high intelligence and it's very noticeable when she goes on her soapbox tirades.
Pistol on Goof Troop is demanding and annoying, as well as seeming to enjoy getting her brother, PJ, in trouble with their parents, one of whom abuses him (though to her credit she usually will try to tell the one who doesn't). She badgers people so they give her stuff and let her play with them, and becomes very upset when she doesn't get her way, while she thinks the rules don't apply to her. It's to the point where PJ (who is frequently forced into intense servitude) considers playing with Pistol to be the worst chore of all.
In Transformers Animated, Bumblebee, while basically good at heart, is also snarky, mischievous (one time he ruined a stunt involving Prowl jumping over his vehicle mode friends in motorcycle form by jumping out and scaring him), brash, impulsive and does not like being called "short".
Various smaller engines of Thomas the Tank Engine are usually cheeky and mischievous to the point where most of them learn a lesson not to run into this trope. Thomas, Percy, Bill, and Ben are common examples.
In The Legend of Korra, Korra's Establishing Character Moment is when (at four years old) she demonstrates her ability to use three of the four elemental powers that she's not supposed to manifest until she's sixteen, busting through a wall in the process.
Korra: I'm the Avatar! You gotta deal with it!
Angelica from Rugrats is a three-year-old spoiled brat who will go to any lengths in order to get her way, or boss around the babies.