Firewalls on consumer routers is not really a firewall - these mostly protect by hiding clients behind the NAT'd IP addresses. And some do some basic packet inspection. But probably good enough because nothing can attack the machines.
If you use the laptop somewhere other than home then definitely have a firewall. e.g. use in public wifi hotspots means you're open to all sorts of threats. And if the laptop got infected, then using it at home means your router's firewall is irrelevant.
If you have Zone Alarm already and it's working then I'd personally stick with it. No harm in having additional protection.
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Zone Alarm - do I actually need it? new
Zone Alarm - do I actually need it? new