Your items are not very highly correlated - this might mean that they are measured with error, or it might mean that they are not measuring similar constructs.
That means that, by things like chi-square and RMSEA, your model is not very bad - but the trouble is that no models are especially bad. Try running a one factor model, it won't be very bad. In fact the null model, which proposes that there are no factors at all, is not very bad - your fitted model only reduces the chi-square by about half.
Your chi-square and RMSEA are good, because you don't have the power to find bad fit. That's why you should always look at CFI/TLI as well. (The reverse is true - very high CFI combined with poorer RMSEA/chi-square tells you that you had a lot of power. A conclusion you can draw is that CFI always works.)
Jeremy