I'm not adding much here, but want to drive home the fact that some of the above comments represent the single best advice you'll ever get. Not just for rafting, but for life. THE BEST LIFE ADVICE YOU'LL EVER GET. Don't squander it.
I had one daughter early, and then another one 13 years later. I didn't do enough of this stuff with the older one, and regret it more than anything. We try occasionally now that she's grown up and has her own life, but it's just not her priority, and it doesn't work out that well. You only get one chance and, as others have said, that door closes at about 12 or 13 years old.
By contrast, my 13 year old daughter, for whom I've made such things a priority, lives for adventure and wilderness, and is completely at home on the river. The BEST thing is that, at 13, she's already a full participant - not just baggage. It's amazing the amount of growth that occurs between 9 and 13. Case in point, I took her and my 9 year old on the San Juan this Spring. She rowed, she helped cook, she set up and broke down the tent by herself, and helped load the boat.
FWIW, we did a lower-water San Juan trip in April with some other families, just before the permit season, because it corresponds with our Spring Break schedule. Perhaps that's another option for you? You'd be assured of a launch. Weather can be touch-and-go, but we lucked out. The other nice thing about this strategy is that the sediment and metals from the Gold King spill will be somewhat settled and aren't being flushed and agitated from spring runoff.
Here are some pics for inspiration, in case you need more convincing: Teaching the 9 year old to row, day hikes and swimming, rapids... smiles. I had the kids walk Government (daughter took picture), but really didn't need to. At low levels, there are other rapids that are actually more tricky than this one.
Let us know what you decide, and how it goes.