Yes, travelling to Kashmir is absolutely safe. However, don’t be shocked by the abundance of military checkpoints, tanks on the side of the road, military trucks and heavy-armed soldiers roaming down the streets.
The distance between Kashmir and Delhi is approximately 842 kilometres. You can take a flight from New Delhi to Srinagar that will take around 1 hour and 25 minutes. While travelling via train will take you 7 hours and 25 minutes.
Ideally, at least a week would be needed to explore Kashmir and its hidden gems.