Electronic – Current Mirror Gain 1.5 with discrete components

It's certainly possible to do this. In fact, it is done quite often in old test equipment. However, it can be difficult to get this to work right as the transistor gains have to be very precisely matched. This is easy to do on a chip as the transistors are physically close to each other and as a result will be built with similar characteristics as well as being thermally connected, but with discrete transistors this is much more difficult. For one, you will need to make sure that the transistors are at the same temperature by physically connecting the cases together. Second, you may need to get a box of transistors and swap them out until you find some with similar current gains.

That difference in the currents between IC1 and IC2 goes into the load attached to Out.

Also the output impedance of a real transistor is not infinite (could be megohms) that will put a limit on the achievable gain.

That circuit is not practical without some DC feedback to set the DC voltage at the collector of Q1 and Q2, as drawn the voltage would either saturate Q1 or Q2.