Can the KMS key rotation be done before 1 year?
Yes but you will need to perform manual rotation. Automatic rotation is done once per year (if you enable this feature) and you cannot change the length of the interval.
Is what I did the correct way to rotate an AWS KMS key? If not what's
the correct way?
While this is possible, it is not the best way to rotate your key (but this is really arguable and it depends on your security policies).
CMK is not really a key. It is more like a logical container for backing keys which are then used to encrypt data keys that are used to encrypt data. What you might want to do is not to change the container (CMK) itself but rather the backing key stored "inside" of the CMK. This leads to the fact that you can still use the same CMK (you don't need to update any code or scripts) but the actual encryption key (the backing key in this case) will be different. AWS will store the old backing keys and it will allow you to seamlessly decrypt data because its stores pointers to which backing key was used for which data (data key really). But this assumes that all backing keys belong to the same CMK.
Also note that this has nothing to do with re-encryption. All the previously encrypted data stay encrypted with the same key it just that the new data is encrypted with the new backing key. If you need to re-encrypt your data, you will need to do it yourself.
What happens to the older objects of the key gets deleted?
When you do it the way described above, your old backing keys are not deleted so you don't need to worry about not being able to decrypt the data. The are still stored withing KMS and they are only used to decrypt the old (corresponding) data.
If you have two separate CMK and you delete one of them, all the data that is still encrypted using this CMK is forever lost (or at least forever encrypted which is kind of the same). Note that not even AWS will be able to help you in such situation. That is also the reason why there is mandatory delay between keys being scheduled for deletion and the actual deletion of the key.