You can use any kind of ring as long as you feel she is worth that ring you have given her. However in movies and in reality many people use their grandmas ring symbolizing that she is a special person.
While it's ultimately up to you, I think passing down a ring that has been in your family is a great tradition, especially if it has been a symbol of your grandparents long and happy marriage. However if they ever got divorced, then it might be a good idea to get a new one.
Is this your first engagement becoz my friends husband gave her a grandmother ring which was 2ct then they divorced and he gave it to the next wife and she didn't want it after 1st wife wore it. I also had another friend who took family ring and never gave it back after their divorce but as long as your gf likes it what does it matter?