Hello!
"Happy-go-skippy" isn't a word that many people use, and appears to be "made up" / invented for the purpose of a comedic moment within the TV show you watched. It appears to be an exaggeration of a commonly-used phrase, "happy-go-lucky", which means "not worried about anything; not concerned; very casual; care-free."
I believe that "happy-go-skippy", as you heard it, was a humorous way for the character to express the qualities of their personality and the level of joy they experience in their life. The character has such a delightful, positive, winning personality; and care-free attitude towards life, that it inspires him/her to literally skip in happiness or jump for joy! Someone who is so pleasant to be around that they are easy to get along with; someone who anyone would want to become friends with. Picture a person so excited about life, that they can barely stand still; someone who may be happy that they smile all the time and whistle a happy tune!