I can't imagine that it's illegal, unless you are collecting eggs from the wild - not really an issue if you are in the US. But there are bigger issues than just getting the eggs when it comes to artifically incubating and hand rearing any parakeet species. As far as incubating, they are a bit more quirky than you typical poultry egg from what I understand as far as tolerating fluctations in temps/humidity.
The babies when they hatch are not like chickens or ducks - they are naked and totally unable to care for themselves. You have to feed them a carefully prepared special formula made for parakeets and then keep them in a very narrow range of temps and humidity. Oh, and be prepared to feed them every few hours around the clock for about 2-3 weeks minimally - not a task for the faint of heart or easily bored. (ie, most kids)
I've got parakeets a-courting now, and am contemplating if i want to try to hand raise the babies once they hatch - but I won't be pulling the babies for at least a few days as they need constant round the clock care if you are hand feeding. It's best to let the mom and dad care for them as many days as you can get away with it and still get a good human/bird bond before you pull them to hand feed.
