I have a Carlo Robelli P304 Travel Acoustic Guitar which comes with a padded gig bag.  

I want to take it on vacation with me to Florida.  

Will I be able to bring it with me to my seat on the plane or will I need to check it in?  

Is the padded gig bag enough or should I get a hard shell case for it? 

Please advise,
You'd be best advised to call the airline first for carry on size restrictions.

I expect the gig bag would be fine as a carry on. But a hard case would be necessary if it were forced to ride in the cargo hold.

We are talking about a fairly small guitar, are we not? I think your basic dread or jumbo would have to go to the hold, not sure about the axe you're talking about.
Yes check with your airline.  Some are more guitar friendly than others.  FWIW  I travelled all over Europe and have made several trips to Hawaii with my acoustic/gigbag/overhead compartment.  No issues.
"Your sound is in your hands as much as anything. It's the way you pick, and the way you hold the guitar, more than it is the amp or the guitar you use." -- Stevie Ray Vaughan

"Anybody can play. The note is only 20 percent. The attitude of the motherfucker who plays it is 80 percent." -- Miles Davis

Guthrie on tone: https://www.youtube.com/watch?v=zmohdG9lLqY