My DS was exactly the same and I completely understand how tricky it can be to find things to give them. Some things that I find good are
- steamed veggies
- sausages (I cut them in half and into little sticks so he can hold them)
- sandwiches (cream cheese, avocado etc are great cos you can slip in some tuna or something and squish them together)
- strawberries and bananas cut into little pieces

I wouldn't worry too much about the fat content of foods you are giving her at this stage, fats (including saturated fats like those found in dairy and yes hot chips) are really important for brain development in the first two years.

HTH