Cutting them is OK. Enjoy them in the house or outside, they don't last long enough either way. Keep your plants healthy during the rest of the year to provide the energy for next years bloom. Cutting the bloom does not take away anything from the plant. I always dead head mine to prevent using plant resources to produce unwanted seed. Al

I've read that if you do cut the blooms off young peonies, leave the leaves on the plant (as much as possible) because they are the "power" source of the next year's increase in plant size & amount of bloom.

It is always a good idea to leave the leaves on any perennial-until they wither. But cutting the flowers will not harm the plant-you want to cut them off at some point, either in bloom or after, to prevent the plant from setting seed-why not enjoy them? They don't last long.
Once the leaves die, cut the plant down near the ground. Safer over the winter, and the new growth comes from the roots so the spent branches are just an invitation to rot and disease.

I would agree with cutting the flowers to enjoy in the house. I would be cutting off the seed pods anyway, what does it matter soon or late? Plant then puts energy into root production, not seed growth.

I also agree that plants need good care over summer with adequate water, a bit of fertilizer, good sunlight, to feed the roots for next years flowering.

I trim my leaves and stems in fall, AFTER they brown up. Usually after first frost. Totally remove all the cut foliage from area. This is so any lurking pests have no place to hide over the winter, get on the new foliage next spring.

You are so LUCKY they bloomed their first year! I just had some first blooms this spring, but the plants are 3yrs old. Were very small to start. Worth waiting for, gorgeous and I ALSO cut mine to enjoy inside!!