Do you think this is a date?? I'm confused :(?

So I'm 17 years old and a guy. A few weeks ago I met this girl (let's call her Jess for confidentiality purposes) at a college meet up. Over their me, Jess, her best friend, my friend, and a few more people separated from the group. We continued to hang out and I got her number (well she gave everyone her number). Then a week later we all hung out again but this time she always stayed with me. Then when I got home, I had a snapchat from her and we snapchatted back and forth until she texted me like a couple days later. We've been talking everyday all day for the past few days and today she asked me if I wanted to hang out Saturday and go to dinner. I was busy so I didn't reply right away. 10 minutes later she sent me another text saying that I could also come with her friends and her Friday if I wanted. I told her Saturday was fine and now we're going to dinner. I'm picking her up from her job and "surprising" her with a place (my decision). She's coming alone and her best friend isn't coming. But the word "date" wasn't mentioned anywhere in the conversation. The conversation was basically:

Her: hey so when do you wanna hang out? (She said it randomly)

Me: I asked her when she's free (she wasn't supposed to be free for a couple weeks)

Her: I can go to dinner this Saturday after my shift at my job (she works at a restaurant)

I didn't reply for a few minutes

Her: or if you wanna meet my friends to you can come tomorrow.

I picked the alone dinner. Is this a date?