Think there might be some confusion here.
The 1Gb specification relates only to the LAN/Ethernet connections, which in layman's terms are the connections on the back of the router for stuff WITHIN your house. So if you plugged 2 PCs in using Ethernet cables, you'd have a 1Gbps (gigs bits per second) connection between the 2 for file transfers (assuming both PCs were capable of that). The Ethernet connection speeds have zero influence on the internet speeds.
As others have said, chances are the line run to your property is copper, running to a cabinet somewhere in the street at which point it'll be fibre to the exchange. This is the standard setup for all providers except Virgin where they have cable to the premises.
It is possible the installer did in fact run fibre to your property, which would be nice, but I'd imagine stupidly expensive. And fast
As for using the router, I wouldn't bother. It won't do anything your current one can't. Even if you could reconfigure it, which may or may not be possible, it'll still just provide Wifi and internet and won't be any faster. And that's before you look into whether or not you currently use fibre or standard ADSL broadband, meaning the new router would need to be ADSl and VDSL compatible.
Lot of info there but hopefully that helps.
The short answer is no, don't bother