Hi D.,
My daughter just turned 2, so she eats essentially everything, but I remember those days - Naomi was really interested in table food, but I was never quite sure what to let her have, and although I don't buy everything organic (I try to for the "worst offenders" like tomatoes, cukes, grapes, peppers), I wanted her to eat wholesome foods as well. So..........some foods that I discovered which seemed appropriate for a 1-year-old which Naomi were: avocado (high protein, healthy fats, and very soft - she still loves chunks of it to this day), chunks of cheese (also soft and easy to eat), melon (canteloupe and watermelon are pretty soft and easy to eat), strawberries (though might not be the best if your daughter is allergy-prone), zucchini (if you steam or saute it until it's soft), tomatoes (I used to quarter the grape tomatoes, and I guess you could peel them, but I never found it to be necessary). Naomi also loved (and still does) applesauce, but I just by the regular, natural kind (no added sugar or preservatives) instead of the baby kind. You can make your own applesauce or even pearsauce, but it's hardly worth the trouble. Sometimes you can find canned peaches or pears or pineapple in juice (instead of syrup) with no added sugar. Alsooatmeal - instead of the baby kind you can make cold, I would just buy quick-cooking irish oats, and add milk, a touch of brown sugar and cinamon or blueberries (which your daughter mind be able to eat, or you might want to cut them in half), and she liked that. At that age I would also give her cut up chunks of whole-grain bread with a little cream cheese or thick yogurt spread on it - she ate that from 10 or 11 months, I think, and has since graduated to peanut butter. I found that if I made a thick soup like split pea, it was something she could easily eat - that's something you can make on a weekend and freeze, or could probably buy an all-natural canned variety. Also, pasta worked well (I buy some kind of whole-grain pasta and she has never complained), usually penne or rotini cut in chunks. And sometimes I was able to find low-salt, organic or at least no-nasty-chemicals-added turkey hot dogs, and cut them in small chunks (lengthwise, then chopped) - or you could try tofu hot dogs if you prefer.
Sorry to be a bit verbose........I feel like I spent a lot of time thinking about this stuff when my daughter was that age, so I thought the info might help.
Happy cooking! ;)
S.