Gibraltar Peak is located in Tidbinbilla Nature Reserve which is located approximately 30 minutes drive west of Canberra. As far as I am aware there is no public transport out this way so you will need a car. Tidbinbilla has lots of walks
There are two main trails to Gibraltar Peak, the first starts from Tidbinbilla Visitors Centre which allows you to park at the Centre and do the walk for free from there. This way takes a little longer. The second and most common route which was our chosen route is to drive into Tidbinbilla via the visitors center at a cost of $11.50 per car and follow the main road until you reach Dalsetta carpark.
We started our walk from Dalsetta car park and was advised that to the peak would be approximately 8.2km or 2-3 hours return and rated Moderate to hard. Personally I did not consider this to be a hard walk, experienced walkers or moderately fit people would only consider the grade to be moderate at best. As for time, we were able to complete the walk by reaching the peak, stopping for photos and exploring then returning to our car via the fire trial in around 2 hours 15 minutes.
A few tips. At the head of the walk just opposite Dalsetta carpark is a log book where it is recommended you fill in your details for safety reasons in case you get lost/injured. In summer be wary of snakes, sometimes they can be hard to see amongst the grass or sticks and can be fatal if you are unable to get treatment in time.