You will just need a new rear wheel. You can get one for a decent price on eBay or VeloMine. You'll also need a cog and a lockring.
Now, you
can just remove the freewheel from your current wheel and mount a cog. This is not recommended but has historical precedent. In this instance you will most likely
rotafix the cog in place using loctite and make sure to mount both brakes. Get some foot retention and use both brakes to stop and you will most likely be fine.*
I don't even use a lock ring to hold the sprocket, I think they are more dangerous than they're worth. I'd rather have the rear sprocket unthread on a descent than to have the chain get trapped and have the rear wheel lock up because the sprocket won't unthread. I raced track for 35 years and never used a lock ring and never had any problems. As long as you tighten the sprocket with a chain tool, it will stay on as long as you don't do a stupid skid stop. Not using a lock ring lets you use the older threaded road hubs.
*I would not recommend it.
One more thing. That frame is generally accepted as a ladies style frame. So I hope you're either a girl or have the swag to pull off riding a girls bike.