it's probably the same one i'm using as well then..
you can unscrew the antennas off the back, just slide back the boot that covers the connector.
did the broken antenna break at the hinge or did the connector break?
if it's not broken at the connector, you should be able to still unscrew it from the router no problem.
i'd get the new router, w/external antennas if possible and look at replacing them if you still run into coverage problems.
here's a list of replacement antennas:
your current router has "N" type connectors on it for the antenna, the other type being "SMA" (a very tiny connector). you can get sma-n and n-sma adapters as well.
this would be a decent replacement antenna for your existing router:
(you'd want two)
using the old router as an 'extender' wouldn't work without changing the firmware, and it wouldn't function very efficiently since it only has one radio in it.
proper extenders (aka repeaters) have two radios in them, one for the link to the base access point and another radio to service local hosts (which operate on different channels). shoe-horned 'extenders' with a single radio have to split their time servicing the local host and then transmitting that information to and from the base AP, all over the same channel. this could cause significant problems with applications that require low latency or use a lot of packets (like games and other interactive media).
if you're considering a wifi router change, i'd make the change first and check out coverage and then decide if the antennas need to be replaced.
if you think you might need to swap antennas after buying a new wifi router, you should look for a new router with replaceable external antennas.