Can an AIT Soldier get married (to a civilian) while on HBL? If so, is this a smart or moronic decision?

A little backstory: We've been in a very productive, happy relationship for 3 years. We lived together for 6 months prior to me shipping to Basic on 17 Sep. Our relationship stayed strong through BCT and now my 2nd week of AIT. We have never had any serious issues, and want nothing more than to be together after I graduate AIT.
There are a lot of service members in her family, so she knows what she's getting in to.
I won't be classed until late January, and I should receive my PCS orders several weeks after that. I believe it will be easier to get our marriage processed before my orders are made, rather than try to get my orders amended after they're made.
Is that accurate, and if so, a wise decision?
Additionally, since I'm in IET status, am I even authorized to get married? Or do I need approval from my CoC? I am unable to find any information about AIT marriages except for marriages between AIT Soldiers.
Any and all input is appreciated. Thank you for your time.