Firstly. If this is your first time camping overnight I wouldn't suggest going for a entire week. Do a overnight first, then a 2 night trip. 7 days solo is a long time if you're not used to it. (Edit. Realised u may have been referring to first time O/N on GNW specifically so above may not apply)
Re safety while camping at gnw campsites.
Generally you will be safer on the trail and camping than you are walking down the street or catching public transport. Less people = less chance of issues.
I think you would be fine camping on the Great North walk. Mostly any uncertainty you may feel will be fear of the unknown rather than a genuine threat.
Take your normal precautions. If anything seems not right then one of advantages is that suburbia is mostly close so a quick exit is possible. Also if you're not happy at a camp spot due someone else being there continue on and find a clear spot in the bush.
The only challenge I've heard of is during weekends and school holidays: on infrequent occasions some of the campsites are used for drinking parties. Never heard of a problem but you may want to avoid this time.
During school times the walk is often used by Duke of edinburgh award guided trips. So you may find 20 school kids with teachers and guides at the main campsites. (So would certainly have no safety issues there)
If you want to be ultra cautious avoid campspots that are drive in or connected to firetrails where people may go for afternoon walks from nearby suburbs. Or just don't set up until night time so no one knows your camping there. (But it's really unlikely you would need such precautions)
If people ask I generally avoid telling them where I'm camping, so having an alternative location which you can tell people you meet on the trail can be useful.
I don't know your financial situation but a Garmin inreach device to allow SOS and two way communication is very handy as works even if no mobile reception. The ability for friends and family to see your live location on a map is reassuring for them. Also will give you weather reports.
If not then consider a PLB as a minimum. (And a snake bite bandage).
The biggest dangers in the bush are tripping and falling or spearing yourself with a stick etc. I would put other people a far away 4th on the threat list. (Snakes second and also unlikely. Bushfires 3rd)
There is a great thread on the great North walk somewhere in this section. Edit Here it is viewtopic.php?f=47&t=28764&view=unread#unread
I'm sure you will have a great time
Just watch the weather re bushfires.