The distance from Pushkar to Chennai is 1900 km. The most practical way is to take a train from Ajmer to Chennai, which is a long journey. Alternatively, you can fly from Kishangarh to Chennai with a layover. The journey takes you across the length of India.
Total Distance: 1900 km by road, 1700 km air distance.
This is a very long journey; carry sufficient food and water.
November to February for pleasant weather.