Genie, welcome to the forum.
Congratulation, you got your first Tree Peony, and it is a beautiful one.
Now, the most important thing is to plant it right; that is, deep enough. I would plant it asap because we already have summer temperatures. The pot is too small, the peony may dry out, etc.
TPs must be planted deep because they need to develop their own roots from the grafted stems, (i.e., scions). It is usually recommended to plant the scion circa 6" deep, but I've planted mine even deeper (e.g., 8") because of our harsh climate.
You need to decide where to plant. Although the full sun is recommended, many people think that dappled shade is better for TPs in our harsh environment. If you want, you could post a couple of pictures of the spot where you want to plant your Koukamon, and we will discuss it with other members of the forum.
Where did you buy Koukamon, if you don't mind me asking?