Echeverias do not do much better crowded. Just like any succulent they like a little extra space, not a lot. Use a pot just a bit bigger than the size of the rosette for best results. Repotting is not tricky if you are careful. The primary danger in repotting lies in watering too soon afterwards. If you use fast draining soil and wait a week to water, the danger is minimal. I repot several Echeverias a week and don't ever have problems. The mother plant in the picture could use a pot one size bigger eventually, but no rush at this point. If you do choose to keep the offset attached, maybe consider repotting in spring.
If you want you can carefully cut off the offset with a sharp knife, allow it to heal for a few days in a bright place out of the sun, and plant it in its own small pot (about the size of the rosette, and wider than deep). Aim for a half an inch or maybe a bit less of naked stem on the cutting. Do not bury the rosette. Put it on top of the soil, but poke the little stub of a stem into the soil. After potting it up, water as you would the mother plant, which is to say when the soil is going dry, not sooner. In several weeks after it has rooted, it will be visibly bigger and that's time to consider a new pot.
My Echeverias of this type tend to offset in the spring and I cut and root the offsets when they are about the size of the one in the picture. By now (early fall) those offsets are well rooted and ready for a bigger pot. The bigger ones are twice their original size. The rooting process does take a month or two, so be patient and do not overwater during the period when the cutting has no roots and can't use it.
Also do your best to provide lots of sun indoors during the dark days of winter... ideally hours of sun, like right by your brightest south-facing window. Echeverias are not generally good house plants without hours of daily sun. If you are in a low light situation, it might be best to delay any serious intervention with your plant until the spring when that's less of an issue. For what it's worth, your plant should totally fill an 8 inch (20cm) pot when it's fully grown, and probably need something bigger if it's got babies attached.
The Echeverias Database