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You can already do that in four different ways:

1. Take a backup, upload it to the new site and restore (obviously, that's what Akeeba Backup was designed to do since day one)

2. Upload to Amazon S3 or a public web location, use Kickstart Professional on the remote server to pull in that backup archive and restore it.

3. Use the Upload to Remote FTP / Upload to Remote SFTP post processing engine to have Akeeba Backup automatically push the backup archive and, optionally, kickstart.php to the remote server when you take a backup. Then you just need to run Kickstart on the remote server and complete the restoration.

4. Use the DirectFTP or DirectSFTP archiver engines to transfer the entire site to the new server. That's something you can also set up using the Site Transfer Wizard. You still need to run the restoration script manually. Counter-intuitively, this is MUCH slowed than the aforementioned three methods and I do not recommend it.

5. BONUS! You can use a CRON job with Akeeba UNiTE on the remote server to automatically restore a backup archive. Combined with method #3 above you can automate the process. Take a backup, it is uploaded to the remote server. A few minutes later the CRON job kicks in and that backup is automatically restored. Once set up all you have to do, from your perspective, is login to the dev site, hit that backup button and wait.