Does 12 V DC to +6 VDC and -6VDC with discrete components require conversion to AC?
It requires conversion to AC, but not necessarily a transformer. Maybe an inductor or capacitors will work fine, depending on the current requirements. 

The easiest thing is to buy a DC-DC converter module with an isolated output or +/- output. You can also use a switchmode power supply chip as an inverting boost converter with only a single inductor. In keeping with your retro-space-age \$\mu A741\$ theme, you could use an MC34063. That could give you +/-12V

Alternatively, you could split the 12V into +6V/-6V. The easiest way to do that is to use a rail-splitter IC such as the TLE2426. The disadvantage of that is that you no longer have ground-referenced inputs and outputs relative to the +12V/0V supply. Whether that's an issue or not depends on your application. You could also have noise issues if the +12V supply is not clean (for example, if it's a vehicle +12V supply).