Welcome, Kimberly!
I have four profoundly gifted kids, at least three of whom are twice exceptional. Life is never dull around here, that's for sure! We homeschool, though the oldest has long since gone on to college, first as a cc student and this past year, living away from home at a small liberal arts college.
My youngest is three. I firmly believe that if a child asks for work, then they should be given it. It really gives the kids a sense of pride and accomplishment to be doing work that they feel is similar to the big kid's work. I remember when my oldest was about nine and my second child just a toddler. One of the older boy's duties was to stack firewood outside on our rack. Our little guy demanded that he be allowed to do this too, and he did, with great relish! It didn't matter to him that he could barely carry a single piece of wood at a time- he was stacking it, and was very happy about doing the same task his big brother was doing. It was very cute.
Likewise, my dd (now 8) begged for her own workbooks when she was two. So I bought her a phonics book and Singapore math workbooks, and she was happy as a clam. Don't be afraid of being labeled a "pushy" parent just for giving kids what they want. Sometimes that's also what they need!