Unless you're flight crew, frequent flyer or there's a solar storm, radiation is not a significant problem. The radiation comes from space in general, and not significantly from the sun, so a night flight has pretty much the same radiation level.
Physicians can assure pregnant women who are concerned about radiation risks during flight that, for casual travel under normal solar conditions, the risk of direct harm from cosmic radiation is negligible. ... The dose limits [based on risk tables generated by the FAA] are set well below levels at which real harm has been demonstrated.
However, unless you're flight crew or a frequent flyer or there's a solar storm going on, radiation is not a significant problem. You'll be bothered more by the cramped space and the airport routines. Get an aisle seat, and take occasional walks up and down the aisle. Also, drink water to counter the low humidity.source: In-Flight Radiation Exposure During Pregnancy (PDF), American College of Obstetricians and Gynecologists.
This page contains the best Q&A about in-flight radiation concerns I've found. (Summary: It's generally safe.)
You can use this online calculator to determine how much radiation your flight would bring.
To give you some perspective, this chart (here's another) shows that one flight across the USA brings you only 40 microsievert, which is one 25th of the yearly limit recommended by EPA, or just a few times more than a day's worth of background radiation on the ground. So if you fly 25 times in a year, you're still within reasonsafe limits.
Physicians can assure pregnant women who are concerned about radiation risks during flight that, for casual travel under normal solar conditions, the risk of direct harm from cosmic radiation is negligible.
...
By referring to risk tables generated by [the FAA] and with knowledge of the recommended dose limits from national and international organizations concerned with radiation safety, [pregnant flight crew members] can make an informed decision as to the amount of flying that they wish to do. They should understand that these dose limits are set well below levels at which real harm has been demonstrated.
source: In-Flight Radiation Exposure During Pregnancy (PDF), American College of Obstetricians and Gynecologists.Notable safety exception:
Radiation levels can be a lot higher, though, during solar flares — bursts of electromagnetic radiation caused by disturbances in the sun's atmosphere. Fortunately, solar flares are rare and last only a short while.
The The National Oceanic and Atmospheric Administration posts solar radiation storm alerts on its web site. Some experts recommend that pregnant women check the site before flying and consider postponing their trip a day or two if a storm is forecast.
source: babycenter.comsource: babycenter.com
But even solar flares aren't that dangerous, according to the Q&A page linked above:
Some measurements have estimated exposures of 100 times the usual exposure while flying which would bring your exposure in the range of a low-level exposure from many diagnostic radiological procedures. Even this exposure would not increase your risk for birth defects or miscarriage, which is 3% for birth defects and 15% for miscarriage for all healthy women when they begin their pregnancy.