Simulations sometimes make strange things. I have Multisim too and sometimes it behaves stupid.

Yes, you have to use a clocked flip flop. It can be RS or JK. It would be better to be a JK with preset and reset inputs too as to have more control on it.

 

Use this JK which can operate at 12V. It has two JKs in one IC, so use only the one.
Connect the output of U1 to a NOT gate and the output of the NOT gate to clock1 of the JK. Then connect Q1' of the JK to the trigger of U3 and the output of U3 to Reset1 of the JK.

http://www.jaycar.com.au/images_uploaded/CD4027BC.PDF

 

Use this JK which can operate at 12V. It has two JKs in one IC, so use only the one.
Connect the output of U1 to a NOT gate and the output of the NOT gate to clock1 of the JK. Then connect Q1' of the JK to the trigger of U3 and the output of U3 to Reset1 of the JK.

http://www.jaycar.com.au/images_uploaded/CD4027BC.PDF

When you say "Not gate" do you mean another IC in addition to the JK? By using a not gate is this to flip the clock signal so as to catch it on the negative edge of U1's output? I've connected also the output of U1A to the "J" input of the JK.

 

Anymore thoughts/concerns/missing resistors? If not, i'm going to order the parts and proto it up.