Moving Router to Better Location

I would like to relocate my FiOS Quantum Gateway into a more central location in my house and just want to understand if this is something that FiOS supports (can be done without a technician) and what is required to do this?

My ONT has the following connectivity - 

Into the ONT

• Fiber from the street
• Power

Out of the ONT

• Coax into a Splitter (One back to the splitter outside & one to the Quantum Gateway)
• Ethernet into the Quantum Gateway

If I wanted to move the router would I need to extend all of these cables to the new location? If I am experiencing slowness lately due to the placement of the Quantum Gateway is this something that a tech will come out and do for me (free / cost)?

Thanks in advance.