I like to paint rocks and things with popular cartoon characters on them. Would this be considered a copyright infringement since the characters are not mine?
In one word - Yes.
Anytime you use the design or character of another without permission, you violate that person, persons or company’s copyright.
Some copyright holders overlook this (or perhaps just never know it was done), while from others you’ll be hearing from their lawyers.
Be safe - not sorry. Come up with your own characters or get permission first!