Something I read suggested that these types of defects are often incubation related.
Cross beaks have been investigated by quite a few people.
Apparently the one which is not genetic (for crossed beaks) is associated with unilateral Microphthalmia & Anophthalmia (abnormal development of the eye). I wasn't familiar with this so I looked it up....here is the link
http://medical-dictionary.thefreedictionary.com/Microphthalmia+and+Anophthalmia
This type, the chick appears normal at hatch & it starts to become apparent at about 1-2 months, fully developing by 3-4 months.
Apparently this type of condition is
infuenced by incubation conditions. To me that does not say
caused by....but I could be wrong?
Other causes of cross beak have been investigated & are said to be hereditory one as a simple recessive, another as comlpex recessive.
The simple recessive was found not to breed true & sometimes showed in 'split' birds. Another was able to breed a bit more reliably but doesn't seem conclusive from what I'm reading here.
One was said to be apparent at hatch the works do not appear to say.
Lots of people have given you their opinion.
As Lildinkem says she's your bird so it's up to you whether you breed her or not.