No, you have a freewheel and the conversion kit you have bough is for a freehub. The freehub you have linked to will not fit your freewheel.
I don't know if you can get freewheel kits with spacing. Most freewheel kits I have seen have the cog close the hub flange - the chain line would be wrong on your wheel.
There used to be an adapter kit made by Brake Therapy that would allow you to mount a rear caliper on a non-disk frame. It's the only adapter I've ever seen that looked reliable enough. I believe they're out of business though.
That would still leave your fork needing to be altered or replaced and replacing your wheels to be disk compatible. So no budget ...
You would require new wheel hubs with a disk rotor mount, and you would need a fork and a frame with caliper mounts.
Once you replace the fork, frame, and wheel hubs, its not economical.
Instead, shout yourself to some new rim brake pads. Good kool-stop ones will improve your braking and it feels like a decent upgrade, for much cheaper.
No, this conversion isn't possible. The 130 version has a different shell than the 120. The flanges are further apart. That's the good way for them to have done it, because if they had used the same flange spacing throughout, that's wasting lateral strength on everything but the 120. If you look at your hub you'll see that there's not really anything you can ...