Is it safe for young kids to take a plane now?

no. i never trust a plane

Air crashes are very rare, but do happen, and when they do, consequences are usually among the nastiest. Terrorism is another threat whose risk is perhaps grater on a flight than on land. Anyways, the greatest threats are probably the most common (my son failed to lose a feet in a mechanical escalator, by chance, he only lose the sandal, but it was frightening). However, given the forum where you are posting, I guess your concern is about radiation during the flight. The main source of radiation during a flight is cosmic radiation. The longer the flight, the greater is the amount of radiation, not only because you are longer on the sky, but also because longer flights tend to flight higher too. Also, cosmic radiation is higher on flights going through the poles. The amount for a single flight is almost negligible as compared with the background radiation your child may receive on a average living place. Only people flying very frequently would merit to have some concerns. That's why in Europe (not in USA, if I am not wrong) it is compulsory for air companies to account how much radiation is accumulating navigation personnel over the time because the amount they accumulate is significantly greater than general population. For pilots and stewards that work mainly on transcontinental flights, it can be as high as 5 to 10 mSv/yr. However, no increase in cancer rate has been observed in this personnel compared to equivalent populations that do not flight (the contrary, in fact), with the exception of breast cancer that is slightly more frequent in air hostesses. However this has been linked more to the hormonal dysregulation due to repeated jet-lags than to this slight increase in cosmic radiation exposure because it does not fit with what was observed in Hiroshima & Nagasaki survivors.

With respect to any increase of radiation on a flight due the Fukushima events, the UC students will tell much better than me, but my view is that it does not deserve the shadow of a worry because background radiation is much much higher than the added burden. People's anxiety towards the unknown is by far much more harmful, and is highly contagious. That's why accurate information is so important. Our body prepares itself to react to what it is perceived as a danger as a natural survival reaction, but when this happens repeatedly or lasts too long, it becomes itself a source of trouble that can be more harmful than the danger it tries to escape. So I hope this will reassure you so you will have a safe and pleasant journey with your child. He or she will benefit from you showing reassurance, it is important for the psychological development too.

Regards.