You are saying router but you mean switch. Big difference in what they actually do (and low-end routers often have a built in switch as well).
There are whole families of network switches designed to work with AVB. You should be asking what people recommend or googling for Ethernet switches that support AVB. Which would turn up results like this...
https://support.biamp.com/Tesira/AVB...ernet_switches
Your budget, how many ports you need, what speed you need (1GBit?) etc are important.