Ahem...
Short answer:
Picnic - bring a kite.
Long answer:
Man, I dated a chick who was 18 when I was 21, and I thought THAT was too young. Guess it's cause I was always the youngest through school, so I tended to date older.
Anyway, as someone who's 32, you know exactly what you want out of this. Whatever it is, you know what you want.
All I'm saying is that if I were 32 and I were dating (ahem) someone who was 20 (you taking her to the carousel? Hahaha! J/k, man, I feel ya)... well, yeah. There's a 98 percent chance I'm in it for the sex. There's a 2 percent chance my 2 percent is already in there. Ha!
But, you're the one who knows her. If you know there's something boiling under that's worth following up on, just keep it light and funny for a year 'til she turns 21. Then you can really start dating outside of the daycare. (BAHAHAHAHA)
Be creative, you're god damned 32. Go on rerun dates from when you were under 21. Or if you're a regular at a pub, take her there. She'll be all like "Wow! It's like going into a club with a celebrity." (HAHAHAHA)
Although, to be honest, I can't imagine that you can't find someone who you'd relate to better. It would be fun with this girl, no doubt. We all know that chemistry is chemistry. But, intimacy might be a problem, if you're thinking long term. She just hasn't met as many people or knows what she wants quite as much. It's not impossible, no. But you will face more hurdles than you need to.
Yup, I just mentioned feelings and long term crap in the DJ forums. But hey, you're 32, and you know what I'm talking about.
It will work out. Good, bad, or sideways, it will work out. Peace, brotha.