How do I progress?

First of all sorry if I ask anything which makes me sound really stupid but I haven't really had a proper relationship before so It's a learning curve.

She's not my girlfriend yet because I haven't asked her but she's not just another girl... It's weird and don't know what's going on but I'll try my best to explain it. I told her I liked her and she's told me she feels the same way too but she says she wants to get to know me a bit better as we don't know each other that well and she doesn't want to rush into as she only about 2 weeks ago split up with her boyfriend of 8 months. I've invited her out on a date so we can do something but we haven't decided what (any ideas?), we've met up I think 2 or 3 times on our own just the two of us but we just walk and talk... I haven't really been in a proper relationship like I said so what should I do next? Right now it feels like we're still acting as friends because we're not on proper dates and we're still learning about each other... Should I hold her hand next time we're out and see what happens? When we hug it's a long meaningful hug not just a quick one and we both say "I love you." not "Love you." and she understand the difference. It's like we're practically together but we're not and I'm clueless and don't know what to do!

Any help would be greatly appreciated!