Wally makes a good point. If the peak current out of the +12 V supply is 1.1 A, there are two return paths: through the virtual ground and directly to the power supply return. If most of the load currents are balanced between the rails, then there might be very little virtual ground current. Only you know for sure.
Separate from that, 2 x 5 V does not equal 12 V, so besides the virtual GND you also need a 10 V regulator. With only 2 V of headroom, common parts such as LM317 and 7810 (if there were such a part) will not work. 5 V +/-0.8 V x 2 equals 10 V +/-1.6 V. That is not very tight regulation, so you probably can get away with a simple "active zener" regulator made from very old part numbers. I can't do schematics right now; maybe someone else will hop in.
What is the circuit powering?
Where are you located?
Where is the circuit going?
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