Something like this should work
sudo /sbin/iptables -t nat -I PREROUTING -i eth0 -p tcp -m tcp --dport 8080 -j DNAT --to-destination 10.1.1.1:80
If you haven't already done so you may need to enable IP forwarding too
/sbin/sysctl -w net.ipv4.ip_forward=1
and to make it permanent edit
/etc/sysctl.conf and set
net.ipv4.ip_forward = 1
As the policy on your FORWARD chain is DROP you will need to allow packets through. I don't think your current FORWARD rule is doing anything helpful so delete it.
Enable packets sent to FORWARD from eth0:8080 to be sent to 10.1.1.1
/sbin/iptables -I FORWARD -p tcp -m tcp -d 10.1.1.1 --destination-port 80 -j ACCEPT
Allow packets to go the other way too
/sbin/iptables -I FORWARD -i eth1 -p tcp -m tcp -j ACCEPT
You mat want to restrict the latter further.