Is my dad's advice good advice?

Ive had only one girlfriend (current) and its going pretty well, but after our second date, my dad told me on the way home from dropping her off at her house that at my age and with *my potential*, I don't need to treat my first girlfriend like shes the one and only. What he eventually told me is that I should try dating more people than one. At this point I really like Tina, and I don't want her to think I don't really like her, but I also don't have dating experience. Also sometimes I wonder if she is dating more than just me, and to be honest it wouldn't bother me as long as we are on the same terms. If she isn't, then I will be OVERJOYED, but if she is, I understand, because to her, an experienced dater, this could just be another typical person to date. What I'm asking is what are the terms of "dating" like this. We spend about one day per week together since we live 30 min. apart, and we are not facebook official because i dont wanna overanalyze or put her in an awkward position. Just let me know if Im being too much of a sissy for not making it super official, or too much of a sissy for not trusting myself in this. Thanks