If you are in Australia an Electrician isn’t licensed to run Ethernet, they must have the required qualifications.

In my town (I am an IT contractor) and it can cost as low as $170 thru to $1400 to run one outlet, depending on how far and how difficult it is to run the cable.

If you decide to do it yourself

• Keep it at least 200mm (10") away from electrical wiring
• Keep it away from Flourescent lighting
• Find the correct connection for your Sockets (what wire goes to what pin)

Even if you run what is called shielded cable (its meant to block out noise/interference) it isn’t infallible.

There is a down side to running copper between buildings - different earths. You are at risk of allowing a lightning strike to the carriage house being carried to the devices in your home and baking them while the ones at the carriage house will survive.

There are some suitable low cost 8Port GB switches with SFP and you could buy a pre-terminated fibre lead to run the distance.