Sounds like a tough walk, but I know as I live in this region that it will be well worth the effort for the scenery alone.
To walk 34 kilometers and climb 1000 meters after Carcassonne is indeed tough. It may be helpful that there is a hotel in Lastours, a little off-path, but at the right distance from Carcassonne. On Day 2 you hit the GR 7 on top of the Col del Tap and from there you can use Topoguide 716 (GR 7 and GR 71) until l'Espérou. I have an edition 1998 which shows plenty lodgings, but there may be a more recent edition. After l'Espérou you use Topoguide 704 until Villefort, and then Topoguide 402 all the way to the Rhône valley, where you will be able to find lodgings without a guide. Menno
Good point.I started to use the "Naismith Rule" on later sections but not this one. Applying the rule generates 11 hours!Also in my experience leaving large towns, Carcassonne in this case, always takes longer than you expect. Another earlier place to stop, claims to have a B & B is Limousis.