So my ID's are in my SQRL app on my laptop or phone. Can I sync my ID's between my laptop and phone? I don't want to be forced to use my phone to scan a QR code on screen for every site..
Can 1Password implement SQRL?
Can 1Password implement SQRL?
That being said storing that key on your (encrypted) mobile only is what protects you.
There is an option to maintain the state of which websites were used to authenticate, but that's only to reset your access should your private key be compromised (or mobile stolen). Then your SQRL app should sync the list of websites with some central location. This would ensure that the day you think the key is compromised, you can reset all access to all websites with a new private key automatically (this is part of the SQRL protocol).
On 1Password, I don't see why not. Gibson made the protocol open source and free.