Courtney, depending on how long you need your cane to be, you might be able to get by with a wooden dowel. Some craft stores sell them in 3-foot lengths, and if you've ever noticed how tall a yard stick is then you might actually end up trimming one down a bit, especially once you add the handle and the tip. (For the record, the actual cane part is referred to as the shaft.) Home improvement stores also sell dowels like that, and a 1-inch diameter dowel would be a good size and inexpensive, especially if you don't mind a straight-shaft cane, and aren't looking for one that tapers as it goes from handle to tip.
Since you already have the handle, you might want to take a look at Walking Cane Company
. They have all sorts of handles, shafts, and tips (as a reference for others looking to make their own canes for one reason or another). Some of their wooden shafts can be rather expensive, but that all depends on the wood (i.e. ebony runs around $340, while your standard red oak, maple wood, hickory, etc. run around $38 - all USD). All of the shafts on Walking Cane Company site are tapered, so for a 1-inch diameter tip you'd need to order a 1 1/4-inch shaft. And they come in two lengths: 35 or 39 inches. So getting a 36-inch long, 1-inch diameter dowel from a craft or home improvement store would really be the best way to go, again depending on whether you want a straight or tapered shaft (of course the dowel will be straight), but the height is good to give you some margin of error when working to put your handle and tip on.
The Walking Cane Company has a $12 tip to fit a 1-inch diameter shaft (which you'll have to carefully shave down a tad at the base, but that's shown in the instructions). The tip is brass (brushed finish, or polished for $3 more) and comes with one rubber "foot" and one replacement "foot", and as mentioned instructions on how to install it on your cane. (Note on the instructions: It talks about using epoxies for fixing the brass part to the shaft, but once you've put the rubber part in place and tightened the screw up through its middle into the shaft, I've found that hot glue works just fine, and you might not even need that if you shape the end of the shaft so the brass part fits on tightly. The outward flare of the rubber "foot" also helps as the widest part is wider than the 1-inch of the brass part, so the brass part can't slip off.)
This is the one I put on the end of my old walking stick some years ago when I replaced the cheap piece of copper tube that came with a walking stick my wife bought for me: 1-inch Diameter Cane Brass Tip
. (Unfortunately I can't use my stick anymore because it was just that - a walking
stick. Thanks to that back injury of mine I need an actual cane that can support a good part of my weight and my walking stick can't.)
To finish off the look you might want to add the Walking Cane Brass Collar
that fits a 1-inch diameter shaft ($5 for the brushed finish, extra $2 for polished). It does put a nice finish on your cane, or walking stick, between the shaft and the brass tip. (I put one on my walking stick and it still looks great. The rubber "foot" never needed replacing and I got a couple of good years' use out of it before I got hurt.)
All links to the items I have above - and lots more - are on Walking Cane Company's main page, either on the left side or as you scroll down. (And for the record, I have no vested interest in this company. I just happened to Bookmark it years ago when I was looking to replace that cheap-o copper tube on my walking stick so I would know where to go back and find them again. There are other sites out there selling cane and walking stick parts, but I found this one to be the least expensive. I'm only recommending them based on personal experience. A Google search will reveal many of those other sites so anyone that wants to can search and compare prices.)
Anyway, Courtney, I hope some of this is helpful to you, and everyone else.