I don't understand the logic of some of these responses. A lathe is the most versatile machine in the shop. Old time machine shops had lathes with milling attachments,but often did not afford a mill. I had a lathe with a milling attachment first for about a year,and made MUCH larger projects than that telegraph key. And,my first lathe was a Sears Atlas. Even it had a milling attachment that worked fine for small and medium parts,especially on brass. Get a larger lathe than a Harbor Freight,though. A Smithy combo unit will do what you are trying to do,though their milling heads are not the most ideal. For you,they'd work fine.
If I may offer a few suggestions about your project: Find slot head screws and do not use Phillips head screws on vintage style work. It is not good practice for the countersinks to be deeper than the top surfaces of the screw heads. They should be flush. And,polish the heads,keeping them quite flat,no rounding off of corners. Take old screws off of old furniture if you have to,but never use Phillips head screws on vintage style work. This is a very important detail. Blue the screws with a torch to a spring blue for an even nicer touch,which was even done in the 18th. C.. They used blued screws in brass hinges. Their brass was all cast at the time,and too weak to trust making screws out of that had to be strong.
Don't use socket head Allen screws. Don't use Allen type set screws. They didn't have them on vintage equipment. Saw off machine screws of STEEL,and with a jeweler's saw,saw a slot. I do this myself when I make vintage type parts. Even knobs in the 1950's used slotted set screws. These little details can make or break a first class job.
I have posted how to make old style microscope/telegraph/scientific instrument style knurls by milling(in the lathe) the knurls with a tap held in the chuck,revolving against the knurl wheel. It would greatly enhance your work to have authentic old style knurl work. You need a lathe to make the knurls and to use them.
Keep all the corners of your work sharp and crisp. do not polish them till they get rounded off. You can rub small blocky brass parts on fine abrasive paper to get them quite smooth. Get some wet or dry paper down to 2000 grit. Work down to this fine grit with slightly soapy water. You will only have to do minimal polishing after that. And,the final buffing can be done by rubbing the parts on flat wood charged with Autosol or Simichrome polish. Autosol is preferred by conservation departments in Williamburg,where I was the master toolmaker.
Look at original work that is not beat up,and see how sharp and crisp they made their parts.
I do not mean to denigrate what you have done,but I can see that you have it in you to do even better. I needed this type of advice when I was young,and simply had not thought about these type of details. This type advice was how I improved my work,though I was already a pretty decent craftsman at the time.
Go to the "Moderators at work" section and look up my brass dividing head. It was all made with a lathe and milling attachment. Look at the nice knurling. They were made with knurls I made,too. Look how crisp the edges are, Yours are mostly o.k.,except for the brass block on top of your key.
