It will take time before any altcoin other than bitcoin cash can make it to $1000. Ethereum can be the next candidate but it might take a couple of years before it reaches that price. Some altcoins possess the ability to make ATH but lacked enough support.
It will not be as long as you think in my opinion. Look at the Dashcoin : he took a lot of value and worth near 600$ so 1k$ won't be that hard to reach.
For Ethereum it is near the same, but slower for the moment, and I'm sure that next year it will be around 600$
