Modifying Transistor Properties in Proteus
I found what to do :)
The problem was that I thought that for every value of collector current the voltage between base and emitter remains constant. But, it was completely wrong. As stated in the Ebers-Moll model, there is a formula for this kind of situations.(The guy with G36 nickname mentioned that in the comments.)

$$
I_S = I_C \cdot e^{\frac{-V_{BE}}{V_T}} = 1mA * e^{\frac{-0.6V}{ 25.86492mV}}
$$

Using this formula, we find
$$
I_S = 8.43E-14
$$

And then the final thing is to adjust this parameter in Proteus. To do that,


Right click the NPN Transistor component,
Select 'Edit Properties'
Tick the box 'Edit all properties as text'
Then append the following line into the text box. (Don't include arrows :D )>> 
IS=8.43e-14


Click OK, and you are ready to go.