Everytime I think I may be seeing the light something comes up to make me rethink it. I have believed that Danielle was pregnant, possibly had gotten pregnant during the 2 month period after being ship wrecked before she killed Robert. But reading your posts and putting my thoughts together on them triggered some questions now I'm LOST again.
Why when Danielle was questioning Sayid did she keep asking Where is ALEX? over and over in different languages? How would anyone know what her child's name is? She has stated that she killed them all and she has never seen the OTHERS only heard their whispering. How do we know there really is an ALEX? Alex could be whatever is roaming the treetops (what many refer to as the monster) remember when Sayid asks her if it's the monster she replies "There are no monsters."
I believe that she is quite sure that whoever took Alex knows what her childs name is.
Possibly because Robert handed the child or possibly even Danielle when she was pregnant, over to "the others". Just like Ethen wanted our little band to hand Claire over.
Assuming of course that 'ALEX' is actually Danielle's physical offspring and not an acronym - like for 'Artificial Life Experiment'. I believe Alex is a person, though, and 'nuff said on that. It's been discussed ad nauseum elsewhere.
First, if the "others" are carriers, then they wern't sick from the disease, but could spread it.
Second, if Danielle gave Sayid the cure, then:
(1) Where did she get it from?
(2) Why would she have feared them being rescued?
(3) Why didn't she give it to her shipmates?
Another important thing to consider is that she never actually states that there is a contagious, infectious disease present. It could just as well be a toxin present on the island.
Why was Danielle questioning Sayid in different languages? Probably because she wasn't sure what language(s) he spoke.
Danielle did not know what language Sayid spoke at first. If you remember, he was hanging upside down and he was mumbling, presumably in Arabic, and only partially conscious when she cut him down. He was still out when she dragged him back to her place and tied him up, and had to wait for him to wake up. As soon as he began to wake up, she began to question, in as many languages as she knew, hoping one of them would be understood.
Or maybe pregnant women/women who've borne children are somehow immune.* Hmm...just thought of that...
Actually, I have a pet theory which goes that 'the Others' have the ability to screw with the minds of pregnant women, and I eventually thought that when Claire returned to the castaways she would eventually go batcrap crazy and try to kill people, and ends up being the castaway which dies at the end of the season.... and then when she DID come back she had inexplicable AMNESIA, which began me thinking, "Hmmm...."
Assuming of course that 'ALEX' is actually Danielle's physical offspring and not an acronym - like for 'Artificial Life Experiment'. I believe Alex is a person, though, and 'nuff said on that. It's been discussed ad nauseum elsewhere. 
and
and 