My phrasing on the title-description is actually chosen quite on purpose in regard of them obtaining renown, namely using [i]is spreading[/I] about word of their actions; in other words knowledge of the Battle of Anaxim has only started spreading, but it will probably take an IC week or more before it has actually become widespread enough for most Rodorians to know of it. Right now their chances of finding someone who has heard of the battle and their part in it are quite minor (it is slightly higher for the other characters, since they are a day ahead), but it'll get there.
The main reason that Aemoten's group hasn't earned any particular renown just yet is mainly due to the lack of someone to spread the word for them... once they leave the borderpost behind and the guards to their own devices, word will probably start spreading in accordance with what the guardsmen know of what has happened, earning them a title as well... possibly. Presuming the guards are left alive and have any real idea of what actually did happen.

As for the campsite the dragon will actually be there; he'll stick with Jillian and Gerald for the time being. He'll be rolled up beside the lake and probably be snoozing a bit if it takes her a while to actually wake up, whereas Gerald will be sitting on a rock several yards from where Jillian is resting and staring into their campfire (with his hood up, now).