With five 7th-level characters, two 6ths, and a 4th-level cohort, you've got very nearly a 9th-level party (equivalent). A juvenile red dragon is only CR 9. Personally, I'd be worried about underwhelming them. A young adult seems like a better choice to me. On the other hand, I'm used to DMing for PCs with very high stats and hp, so I'm probably a little biased.
By the way, I'm currently in the middle of statting up the "typical" feat, skill, and spell selection for dragons of various ages and types. I've got Black, Blue, and Green done and am working on Red even now. It's an HTML file (in tables), so I can't effectively post it here, but if you're interested I might be able to post it on my site and provide a link (but I have no FTP access currently, so I might not be able).