No, it's only up to 300Mbps. If running IPS or VPN, then even lower.
You need the new 5512-X for 1Gbps and much bigger firewall if you want 1Gbps VPN or IPS throughput. There is a handy table on this webpage:
http://www.cisco.com/en/US/prod/collateral/vpndevc/ps6032/ps6094/ps6120/data_sheet_c78-701253.html
However, it's only a problem if you've purchased over 300Mbps bandwidth on your new 1Gbps bearer. If you've purchased 300/1000Mbps, or lower, then you'll be fine for all non-VPN/IPS traffic.
The 'Security Plus' license will increase 2 of your existing ports from 10/100 to 10/100/1000. And you're likely to need a memory upgrade to facilitate the IOS upgrade. But again, do you actually need this? Is your Internet bandwidth over 100Mbps? If not, then ask your ISP if their NTE device will autonegotiate down to 100Mbps port speed.