Hairbands come in many different colors and sizes. Use fatter bigger hairbands for thicker hair and styles. Since baby and toddler hair is so fine, you will need to use the tiny poly bands or these:As her hair gets thicker, you can use bigger and thicker bands, but don't get rid of the little ones, because they are still useful for styles with small sections.
Clear poly bands are good for styles where you want to hide the band.Try out some different brands to find what you like best. Some brands retain their stretch after a day in the hair and can be used over and over. Others stretch out and need to go in the trash. Some pull and break the hair more than others, and some slide around more.
Do not use the office kind of rubber bands in your daughter's hair because they will pull and break her hair (and hurt!).