Can my 6mth old eat diced food if she doesn' have teeth yet?

Yes. Be sure these are soft and smaller pieces.They swallow everything at this age.Make sure not to traumatize your child and develop fear for solid food! some children do , once they get to choking and gagging the bigger pieces or something stuck in their throat.They will prefer liquids over solid until they have confidence again and this might pose an eating problem later.
Cheerio Rule. A cheerio placed in the mouth will quickly dissolve from the saliva exposure and presents no choking risk.If the diced food is soft and small sized, it should likewise dissolve. Think-is it like the cheerio!
Why bother. Baby food 4 -5 decades ago was used to make up the deficiencies in home made cow milk formula. Today we know that breast milk or formula contains all the nutrition a baby needs in the 1st year.Semi-solid foods off a spoon are just a way to transition a baby to table feeds. There is no hurry & no need to push baby to any feed they are resistant to. When baby is ready for a new texture they will.