Anna will probably also have a weak immune system. Not just because she's a toddler, but because of her own situation
Karl-Oskar and Kristina are really poor, and due to a crop failure and having very little food (which is why they Emigrated in the first place) which led to the Anna (and the other kids) to being Malnourished, making them more likely to be sick (and since the series is set in the 1800s, There could be Terible illnesses)
also, random fact but during the 2nd half of the first book, Kristina gets Typhoid Fever (which causes her to have a severe Nosebleed) and survives. She almost died tho.