One of our now-initiated sisters had the same thing last year - she was first degreed in May and initiated in November. First of all, welcome, and its great that you're so excited!
In my chapter we tell girls the same thing, that they're allowed to wear letters but that some of the older girls might "feel weird" about it - one of the primary reasons is that traditionally your big makes you your first set of block letters. Do you have any old t-shirts that they gave you? You could wear those. Or maybe as a treat to yourself you could order some KD jewelry until then - that's what I did. And tell whoever you want that you're a Kappa Delta new member (and not a pledge!)
As for what you can do over the summer... I'd second the idea of just interacting with KDs online, and maybe learn a bit about KD history. If you're really bored, start memorizing the purpose, creed, etc. out of your Norman Shield, because you're just going to have to do that anyway
