Should I let my family stop me from dating someone I really like?

I've been talking to this girl for a couple weeks now and things are going great. We feel like we are ready to take the next step and begin dating. One problem though, my family is against us dating. The only reason they give me is that she's too young.. Her family is all for us dating and have accepted me as part of their family and I'm worried my family won't do the same if we date..So should I listen to my heart and be with this girl even though my family is against it or should we just remain friends