Welcome to the forum, Connie, Luna and daddy! And OMG, I don't blame you one bit for getting her/him! You would have had to have had a heart of stone to be able to resist him/her! Now, I suggest you have Luna DNA'd before you decide on a feminine name or choose one that is unisex unless you don't care if you end up with a boy named Luna!
Wolf and Liz gave you good pointers in terms of getting them to eat a good diet so I will only add a couple of things. The best time to get them to try new food is early in the morning about one hour after the sky is lit enough that you can see fairly well without artificial lights, this time of the year means about 7:30 am. The trick is to give them a good dinner (I give them enough of their seed mix to fill their crop and a tiny bit extra -just in case they are hungrier than normal) and take away their food bowl after they fall asleep (which should happen as night falls naturally and without any artificial lights on -especially electronic screens which give out a blue light that keeps them awake). Then, when dawn starts, the bird will wake up and, about one hour after this, it will be good and hungry and, as there is 'no better sauce than hunger', if you eat produce in front of her (sit down at the table, if you wish), she will want what you are eating (don't offer, just talk to her and eat as if you did not care) and, when she does, offer her some (just make sure it's a 'fresh' piece of the side of the fruit or whatever where you have not touched with your mouth -human mouths have bad bacteria that can make them sick). Now, I know that eating raw produce early in the morning is not something that we enjoy but you can start with things that are not too bad like apples, oranges, grapes, etc. GCCs are mainly fruit eaters in the wild and normally eat a portion of fruit larger than what we would think it's a 'good' size for a small parrot. One thing that I find useful is to use the same phrase all the time (it doesn't really matter what you choose to say, only that you use it ALL THE TIME) because, in time, it becomes a clue for the bird that means: "this food is good and you should try it!" I have a Senegal that says: "Eat it!" whenever he is hungry, somebody is eating or if I am serving food - I did not teach him this phrase as I say something different but somebody in his previous life did and he learned it so well, he actually tells the new birds to "Eat it!" when I am teaching them to eat new food
The sharing of breakfast has two purposes: one is to teach them to eat new foods by showing them that the food is good and not dangerous but another one (and as important as the first one) is that it creates a bond between the bird and the humans. Parrots always eat together (in flock) and, although some people believe that their foraging is work, that is not the way birds regard it. To them, foraging is a social occasion and one that they enjoy beyond the fact that their hunger is appeased so, when the human eats with his/her bird, the bird understands this action to mean that both are part of the same flock... that they 'belong' together.