Right, two things here: First, the Amiga's physical connector is different from VGA, although you can get simple passive adaptors which give you the standard female VGA socket Click for example. Second, while with that adaptor you now have the signals on the correct pins, you still have the wrong frequencies on the output by default. The A1200 can use some higher frequency screenmodes which should work on most VGA monitors, but anything that bypasses these settings (most games for example) simply won't work.

More complicated adaptors are available called scandoublers which take the video signal and double its frequency as well as providing a VGA connection, and all software will work fine with these as it's a hardware rather than software frequency change. But they're a good deal more expensive as a result. External ones connect to the monitor port on the back of the A1200, internal ones connect directly to the chips inside and therefore usually give better quality, but can be tricky to fit. You might have to scour eBay for one...

As for those video-VGA converters, they'll work fine too, but the video out from an A1200 is actually pretty poor quality, so you wouldn't be making the most of it.