Catrine, of course you don't give up.
10k is just over the 6 miles and a 5 x 10 min miler comfortably would enable you to do it faster than me tomorrow. With six weeks training you can build on this to ensure you have a 6 mile+ run in you already and give you a psycological boost on the day to treat it as a race.
You can then find half marathon schedules on the internet for beginners, and intermediates. For example, I shall follow the Bath Marathon website one from late December to mid-March(if I get a place).
A marathon in 2004. Well, you have plenty of time compared to many and all your present training is good stuff towards that goal. Take one step at a time and after the half you can reassess the goal.