It may actually be a very simple answer:
"Tutti Frutti" is the name of an Italian dessert, and it translates as "all fruits". The dessert is a collection of many different fresh and candied fruits and maybe ice cream. The American version typically contains fruits soaked in alcohol, usually brandy. (I've been exposed to all sorts of Italian foods in my life, but never remember seeing this one!)
Also of note, the dictionary says the meaning of "tutti" is: "with all voices or instruments performing together —used as a direction in music". Although this definition probably isn't the one referenced by Little Richard, it's good to know ("okay, bandmates, this time let's try that song more tutti!").
I believe that "tutti frutti" in the song is meant to say, "These girls - Rudy, Sue, and Daisy - are like a sweet mix of tempting and possibly liquered fruits". It's a metaphor. :) But I am up for other interpretations, of course!