Hopefully your peonies are ok. It is not good to mulch that deep over a newly planted peony crown. You can put mulch that deep or deeper in the area surrounding the crown but putting more than maybe an inch on newly planted peonies can lead to the crown rotting. It would be a good idea for you to carefully remove the mulch from where you planted the peonies then replace around the plants.

You may be able to see pink or white buds emerging from the ground already. As to when peonies should emerge is up to the individual peony as some will emerge early but the flower buds will not expand for at least a month. Some will emerge with flower buds that look like they should bloom at any moment. Don't be too surprised if you have no blooms this year and only a few next year. Some peonies take a while to develop the root structure necessary to support blooms.

When we lived in Eastern Ontario, I always planted my peonies with the buds about 2 inches below the surface. I never mulched and the peonies thrived. Although I plant them just at the surface in our climate here, I don't mulch over the crowns at all. They need the cold in order to do well. Also, my understanding is that they prefer a slightly alkaline soil. Pine and fir needles are very acidic and, as they break down, they will acidify your soil. So, I agree with maifleur - get the mulch off of them. They probably won't need staking for the first year unless you see they have flowers forming.

Those tender new buds under the pine needles are really easy to break off. If the pine needles are dry I would use a blower to remove them, if wet I would use a stream from the garden hose. Al

I'm in zone 5 and my peonies have started to sprout and I've never covered them with mulch or any thing else and the come back every years bigger and better

Here in my zone 5, peonies are up anywhere between 1" and 5" depending on the location. I have never used mulch, but this year I have put down a "very" thin layer of black shredded bark because it really shows off the plants and adds a lot of continuity to the garden. It also covers up a lot of small stones that we are cursed with here.

Don't think of the small stones as a curse since they provide pockets in the soil to keep it loose and the stones also provide a mulching effect both heating and cooling the soil.