Gatsby suggests that her wealth is a defining and intrinsic aspect of Daisy's character.
What you can assume from someone having a "voice full of money" is that their wealth affects their being in a lot of ways, as deeply as their speech:
- thanks to access to education and literature, she probably has a varied vocabulary;
- because she was brought up in a respectable family, she probably was taught to use decent language and does not say any vulgarities;
- she probably has a lot of confidence due to her high social status, and speaks in a poised, assertive way.