Error resolving hostname

[#1]

I am using OS X and many programs check my machine's fully qualified domain name while starting up.
It seems there is an issue with AAAA lookups.

$ dig A macbook-pro.lan
macbook-pro.lan.        1429606190 IN   A       192.168.1.2
;; SERVER: 192.168.1.254#53(192.168.1.254) 

But if I check for the IPv6 record:

$ dig AAAA macbook-pro.lan
;; Warning: Message parser reports malformed message packet.
;; SERVER: 192.168.1.254#53(192.168.1.254)

I don't get an answer.
It seems like something is wrong with the DNS server on the router.
Can anyone help with this issue?

[#2]

Does your router support IPv6 and is it switched on?

[#3]

I'm not sure but I just received my Plusnet router this week. It's a Sagecom model.
I would assume that most routers support IPv6 even if the ISP isn't yet allocating subnets.
Is there any way to view the router's logs?  I see I can access dsldevice.lan/expert_user.html but it doesn't really give access to logs etc.
This is causing lots of problems for me because important programs are starting up slowly.

[#4]

Try disabling IPv6 on your client machines and see if this makes a difference.  If you really *must* have names resolving on your local LAN you'd be far better off running a local DNS server rather than relying on your router.