Since the gas is already gone and there's nothing to be recovered, there's no legal reason you can't do it yourself. I suggest you price the line and then decide if you want to do the job.
It doesn't sound to me like you'll save much money, though.
I don't know which line you're referring to, but ALLDATA lists the price of the discharge hose at $111.05, and the suction hose at $318.52. Labor to replace either is listed at 0.6 hours.
Then you'll need to evacuate the system (basically pull all the air and moisture out of it), which you probably don't have the equipment to do; and then recharge it. ALLDATA lists the time for evacuation and recharge at 1.4 hours (most of which would be spent waiting for the evacuation step to finish, so the shop may or may not charge for that whole time). And then there's the cost for the refrigerant itself.
At $390.00, if the dealership will give you credit for the $100.00 "diagnostic charge," it doesn't sound like you're going to save a fortune doing it DIY unless you have the wherewithal to evacuate the system, or know of a friendly neighborhood mechanic or gearhead who's willing to do that part of the job for you. It's not high-tech: It's basically just a vacuum pump and some lines and gauges to make sure you get as close to complete vacuum as possible. It usually takes between 30 minutes and an hour. But it's not the kind of equipment most people have laying around.
So if the dealership deducts the diagnostic fee from the cost of the job, then probably letting them do the job is your best non-DIY option. I don't think too many decent private shops will beat $290.00 for parts, labor, and refrigerant. (But ask around anyway.)
If you do decide to go DIY, you're looking at the cost of the line plus the evacuation / recharge cost. You'll probably pay for the whole time plus refrigerant if that's all you're asking the shop to do, so assuming 1.4 hours @ $75.00, you'll be talking somewhere around $105.00 for the labor plus whatever the refrigerant costs. Your state also may have various fees that the shop has to tack on.
So maybe you'll save something going partial-DIY, but it won't be a fortune (again assuming that the dealership credits you for the diagnostic fee).