Just like in every other areas of child development, your child's rhythmic development will vary and will not follow a strict timetable.  For this reason, we don't put ages on the following chart, but keep an eye out for the different stages.  Remember, your modeling is the most important thing you can do for your child.  Clapping, playing percussion instruments or moving to the beat, being sure to accentuate each beat is one of the best things you can do to promote your child's progress in this area.  Below is a chart of the stages of Tonal and Rhythmic development.  Also check out the two articles following.

 

Tonal Development

Child “coos” or briefly intones slight descending patterns, usually around a one-pitch center.

Child sings songs utilizing skips and leaps away from one pitch. The pitches she or he sings are not the exact pitches of the song, but the direction of skips and leaps represent the song’s correct melodic contour.

Child sings some parts of the song correctly. Those parts may begin the song or progress to a resting pitch at the end of the song.

Child sings most parts of the song correctly and/or in tune.

Child sings entire songs correctly and in tune.

Rhythm Development

Child responds to music, but the movement is undefined and irregular.

Child moves with a characteristic gesture and/or songs with a characteristic pattern of rhythm. That gesture or pattern usually does not synchronize with the beat of the music she or he is hearing.

Child moves or sings with a consistent tempo. That tempo is usually different than the tempo of the music she or he is hearing.

Child’s movements often coincide with the beat of the music she or he is hearing or creating. She or he sings parts of the songs in the correct tempo and meter.

Child’s movements always coincide with the beat of the music she or he is hearing or creating. She or he sings entire songs in the correct tempo and meter.

http://www.nbcnews.com/id/8075422/ns/health-childrens_health/t/parents-can-help-babies-develop-rhythm/ 

 http://www.education.com/pdf/musical-development-early-years/