At seven months old... I won't let a bird sit... they are still growing and maturing both physically and mentally... and during broody sitting their digestion and metabolism are way slowed down.. Best way to benefit my flock is giving everyone the best start possible. IF I do let a young broody sit... it won't be for the whole 3 weeks to hatch and usually includes an early on adoption.
Collecting eggs will NOT be enough in most instances. Some broody's will sit on air for the entire time with no regard for themselves or anything else and STILL need to be broken after sitting there losing condition... they are more susceptible to parasites and such as well.
I also employ wire bottom, elevated kennels... but have discovered zero difference in time spent broody between those and the ones I break in a grass, open bottom pen.. with no bedding... which I resorted to after one large fowl hen had been in the wire bottom breaker for 10 days and I was almost broken! 72 hours is plenty for most birds... but all are individuals. Ones broken in open bottom pens do go in the wire kennels at night.
Ridgerunner always has wise input.
I agree she WILL be broody again, and I would plan ahead for when it's convenient for me... come spring or whenever. Girls who go broody very young are often EXCESSIVELY broody in my experience.
Keep in mind it reduces the amount of mating females and your ratio is already close. It also occupies the box other may want to lay in... which leads me to in case you didn't know... save ALL the eggs you want to set and set them at the same time to avoid staggered hatching. AND be sure to mark clearly (not pencil) the eggs you do set so the nest can be checked every evening and have any new deposits removed... again to avoid staggered hatch and give the best chance possible to the ones you started with.
A sitting hen equals about 8 weeks or more on average of NO eggs from that hen. And some of my gals go broody literally EVERY 3rd egg they lay... EVEN if they just finished raising a clutch.
Some people do fine with winter hatching... even in cold climates. And Thanksgiving babies WOULD be awesome!

But as a first encounter... likely wouldn't be my personal choice. I will also make a quick note about having chicks in your flock effecting what feed you should use... Since I ALWAYS have broody's and chicks, and roosters... I stick with 20% protein flock raiser and oyster shell on the side for active layer. I NEVER switch to layer as it doesn't have enough protein for growing chicks and too much calcium for anyone not laying. A starter feed might also be OK. Broody's rock, but they certainly are NOT responsibility free for the keeper. When they first bring them out I always have to spend the first week or so making sure I am home to help teach them go up the ramp in my coops that require it to get inside. Though mums will usually sit at the bottom, I have found when enough can make it up, others are left behind still. All set up are different and so are all hens... and their chicks.
Congrats on your first broody, and the prospects it brings!