That's a beautiful stand of rudbeckia--you're doing a good job of nurturing it.  I agree it looks too big for that spot, and, yes, you definitely can and should divide it.  However, I would wait roughly a month before doing so, when the weather is a little cooler.

Here is some general information on perennials from Extension, https://extension.umd.edu/resource/perennials, and here is more specific information on dividing perennials from Clemson University, https://hgic.clemson.edu/factsheet/dividing-perennials/ 

A couple of tips.  Water the mother plant well before you start digging it up, as this will both ease stress on the plant and make it easier for you to remove and manipulate the root ball.  After watering, dig up the entire plant.  Once dug up, sometimes the plant naturally falls apart into clumps, which you can use as the new starter plants.  If, on the other hand, the plant comes out as a single mass, you'll have to divide it manually using a sharp-edged spade or shovel.  Cut it into whatever number of good-sized clumps seems appropriate.  Eyeballing your photo, I'm guessing you could easily generate three or four new plants.  Sometimes it takes a bit of effort to divide a large plant like this, but don't be afraid to use some force--the plant will recover.

Since this plant did so well at the spot by the steps, I certainly suggest replanting a portion of it here.  For the other clumps, you can plant them in other areas of your yard that get light similar to what you have now.  If you don't have room to replant all the pieces, or if you want something other than Black-Eyed Susans, give them away to friends and neighbors--maybe they'll give you different plants in return!

Your current plant has done so well that I imagine you used good planting techniques, which I would encourage you to replicate.  To briefly review, before dividing the mother plant, prepare the soil in the new location(s) first, removing weeds and other undesirable plants, and then adding in  lots and lots of compost. Dig the new holes nice and deep so that the transplants have plenty of room to spread their roots.  You can do this soil preparation in advance of planting, even several weeks before planting.  However, once you start digging up the existing plant don't delay planting the newly-divided plantlets--get them in the ground as soon as possible, ideally the same day.  It's a good idea to do this work late in the afternoon or evening, so that the new plants have a cool period in which to get acclimated before enduring the heat of another day.  Scheduling this work just before a stretch of cloudy or rainy days is particularly useful; avoid replanting just before a major heat wave.

Best of luck.

Bob