You can use the compareFunction function with String::localeCompare() on the target keys:
const targetArray = [
{ targetKey: 'March' },
{ targetKey: 'Jan' },
{ targetKey: 'Feb' },
{ targetKey: 'Dec' }
];
targetArray.sort((a, b) => a.targetKey.localeCompare(b.targetKey));
console.log(targetArray)
And if you don't want to mutate (modify) the original array, you can clone it with slice() and then sort the cloned one.
const targetArray = [
{ targetKey: 'March' },
{ targetKey: 'Jan' },
{ targetKey: 'Feb' },
{ targetKey: 'Dec' }
];
let res = targetArray.slice(0).sort((a, b) => a.targetKey.localeCompare(b.targetKey));
console.log(targetArray)
console.log(res);