One of the most important elements of singing is a strong sense of rhythm and the ability to place notes anywhere in the bar effortlessly. Regardless of whether you read music well, or learn primarily by ear, it is essential to develop this ability. This is best done by doing exercises which concentrate purely on rhythm rather than pitch and rhythm.
This example uses only one pitch but contains quarter, half and whole notes. First clap the rhythm while counting and tapping your foot on each beat. Once you can do this, sing the notes using the syllable da while tapping your foot on each beat. Make sure your foot stays independent of your voice. If you do this for a short time each day, you will soon feel more confident with rhythms using these note values.