I think south Alg is a great choice for camel trekking - it's the real thing, nothing like the 'blue cheche' scene in Morocco or Tunisia. Mori would be my other choice, though never done it there.
As far as I know the tassili n'ajjer plateau is not accessible to pack camels.
Tours use mules which can better manage the stiff climb at the beginning with full loads.
However you can certainly do camel treks west, along the base of the plateau to Essendilene, or out into Tadrat to the SE. Any local agency can lay on these regular itineraries, but you may be better off bringing a group.
Essendilene won't be totally satisfying IMO as you won't always be far from the road, but it is a beautiful area with cliffs and canyons to the north and Admer dunes to the south.
Other good areas include Tefedest (may try that next year), Immidir which I have got to know well (check the links at the bottom of this page
). The good thing with Imi is that cars cannot follow; great to be away from pistes.
Hoggar/Assekrem I will be doing this winter though suspect it may be a bit stoney and grim. But it will be a fun way of getting to Assekrem.
If you want to try and DIY I can give you a contact for a Tam agency (speaks bad French only and very slow to reply though not all agencies even manage that much). I would say a week is a bit short. The 12-day Immidir walk is just right for a first timer, but once you get into this sort of travel, twice as long is better.
Alone I suspect you will pay at least €100 a day but I dont think it's something you can just organise by walking into an agency office in Tam. Very often the camels are miles out in the desert and so are the crew.
Normally the best way would have been to join a French agency who offered a whole range of routes in Alg last time I looked, but I think the French are excluded from Alg now by their govt - and that is what has really killed tourism there.