If you wait too much longer you will have warmer weather to deal with that can be damaging to your plant, and the longer you wait the more likely you are to damage the leaves from dividing, transferring, and replanting.
I love perennials because it is a cost that you pay for one time and it comes back year after year. More times than not, a perennial also means lower maintenance and often little to no watering throughout the entire summer.
Specifically in my yard I have hostas and sedums that grow over time and are able to be divided without harming the plant. With only investing in a few plants, you are able to fill in a large area in a matter of a few years. I got lucky and got most of my original hostas from family members who had existing strong plants, so it also helps to know the hardiness of them when possible.
Seedums are another favorite plant of mine. These are slower to grow than hostas. In the late summer they get a really pretty purple flower on the top, but the foliage looks nice in the spring, early summer, then late fall and winter after the flower is gone.
Just make sure when you are transplanting your plants, you dig a hole deep enough to set the entire dug up plant and roots in, and make it wide enough that it will fit with space around it. You will want to fill in the gaps with soil then lightly pack it into the ground. I usually use my foot to stomp the transplanted piece into the ground. Plant before anticipated rain or make sure you water the area if there is no upcoming rain!