I can't tell/don't know if my DD is "gifted" or if I am just exposing her to materials other parents aren't.
You are correct - it's way to soon to know for sure. Just have fun doing what comes naturally to you and DD.
Does my DD learn things quicker and absorb more, or is it just that she is exposed to these things that other kids aren't? Can other kids learn this stuff too and they are just not exposed to it?
Probably some of both. I believe that Mothers know in their hearts what makes their child happy. And Mothers want to make their little babies happy. If you were Mom to some of these other children, you would suggest some things, and the child would indicate if she or he was interested in some subtle way and you'd move on to suggest some other types of activities.
I've really valued the opportunity to watch my son's friends grow up. They each are different in their interests and beautiful in their own way. One friend is super at figuring out how to 'add fun' to any play. Each child IS a gift - it's true, and yet not all children are gifted.
I was very interested and confused about this topic when my son was a toddler and preschooler. I was proud that I had 'made him this way' and sad that I had 'made him different from his peers.' I wrote a few letters to the editor sharing my 'fabulous ideas' for fun toddler activities. It used to drive me nuts, specifically, that all the peer moms read only simple books to their children. If only they realized that 3 year old could love books like Wizard of Oz, and Phantom Tollbooth. Over the years I look back with incredulity that I really believed that other 3 year olds were going to sit still for those sorts of books. I remember reading 'The Lorax' during Dr. Suess week at my son's daycare. I still shake to think of the longest 15 minutes of my life! DSs sat in my lap and lectured the 3 or 4 year olds on the meanings of words or phrases that weren't obvious, in the same exact intonation I used with him for that purpose, as if this was the most interesting thing in the world, and wouldn't they feel great to learn this? On every page. The peers were struggling to sit still, and clearly (to me, not to DS) wanted it to be over! I found it so painful to keep going, and tried to keep DS from 'contributing' because it was so very clear that this wasn't working for the other kids. I think I was having a flashback to my school days when my peers looked at me blankly. I asked myself: "Why hadn't I known to read 'hop on pop?!?"
Being inidentified gifted can make a person do dumb things. DS was as convinced as I was that his peers would love the story and the 'insider tips' - it was heartbreaking. I wished that a hole would open in the primary colored rug and I could dissapear into it.
Later I got to have more conversations with his friends, and I realized - My genetics had way more to do with it than my parenting. It's very common for little apples to fall nearby their trees. Now I take pride in my parenting for how my son's character is turning out, and I'm super proud of that. And I do include 'what he does with his natural abilites' as part of character.
Hope that helps,
Grinity