If you have the equipment and the knowledge, it's not a problem.

But like anything, there are right and wrong ways to do things and, because A/C is a highly specialize aspect of car repair, I would not recommend DIY unless you know what you are doing.

Yeah, the nut and bolt turning is easy, but you need to recover your current refrigerant charge (venting it is illegal and WRONG), you'll need to evacuate your system (you'll need a vacuum pump for this), you need to replace your dryer, you'll need to charge the system with the correct type and quantity of refrigerant oil (use the wrong amount, or type and you ruin your new compressor) and you'll need to charge the system with the correct type and amount of refrigerant. You should also maintain hermetic cleanliness while doing all this and you should minimize the time your system is "open" to the outside world.

None of this is impossible for the DIY, but you need to be aware of a whole new set of important facts and procedures when you are dealing with A/C work, versus nuts and bolts mechanics. It is kind of analogous to doing mechanical work on a car versus doing electrical work on a car. Any DIYer can do car electrical work if they have mastered car mechanical work. For electrical work you need additional equipment (multimeter) and some additional troubleshooting skills (you need to think in an electrical mindset). Same thing with A/C work, you need additional equipment (vacuum pump, recovery unit, gauges, etc.) and you need to think using a different mindset.

Good luck.