Just about anything you eat is OK for her to eat too - as long as it's not a choking hazard, and it's not a known family allergen.
When our 3.5 year old was born, we were told to watch out for certain foods. At our daughter's 1 year appointment last March, the Pediatrician had changed his opinion based upon new guidelines from the American Academy of Pediatrics.
Here's what they recommend for a child your daughter's age:
http://www.healthychildren.org/English/ages-stages/baby/f...
Babies love to chew. We'd cut pears/apples into thin strips for both kids, and they'd gnaw on them until they had barely anything left.
Try to stay away from anything canned - fruits or vegetables. They're VERY high in sodium. Fresh is always best, but frozen is much healthier. Our kids, at that age, loved frozen Mixed Vegetables.
We did a lot of thinly shaven ham/turkey from the deli and American cheese for lunch. Grapes were good around that age (our kids always did well with them whole, but you may want to cut in 1/2 or quarters). Blueberries are great and really good this time of year (best price is at Costco/Sam's Club).
As a snack, Goldfish and Graham Cracker sticks are really good. Cereals such as Chex, Kix, Cheerios, Crispix are not as high in carbs and easy for them at this age.
The other savior has been string cheese. The mozzarella seems to have the lowest fat content and is easy for them to hold/gum to get through.
Good luck.
Just remember that the former opinion of staying away from certain foods has really been reversed in the past few years - anyone still telling you to avoid things is not up to date on current policies. BUT, still check with her pediatrician to be safe.