I should also mention she told me that I am actually the first person she has met online. How should I organise another date very soon? I would like to see her again before anyone else does as it will probably make me look bad in comparison if she has a better time with them.
How should I go about organising another date quickly without appearing too needy or keen?

Any quick advice on how I should go about arranging a second date?

Invite her to JOIN you somewhere cool...just to "hang out" near your place, ask her to stop and see your new goldfish when done. If she is carrying a bag large enough to contain overnight items... your objective is clear.

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They call me the cat whisperer, cause I know exactly what the pussy needs.

I’m getting mixed signals at the moment (or none at all). Her last message made her seem keen in seeing me again so I told her we should do it soon and asked if she was free this week. I haven’t heard from her since and I’ve noticed she has been using her online dating profile a lot. Before we met she messaged me frequently and was doing most of the chasing however since then we’ve only exchanged two or three messages. Bit confused as to whether or not she’s interested, she could have easily hinted she wasn't interested or even suggest 'lets just be friends', maybe she is just keeping her options open? Given how awkward our date was she is going to have much better time with anyone else she meets hence why I suggested we meet soon. I think this one is bound for failure which is a shame as she seemed pretty awesome until we met.

What do you think guys?

Move on and stop worrying about it.

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They call me the cat whisperer, cause I know exactly what the pussy needs.

Yeah I will, think the best thing to do is meet up with a few other people and maybe later assess where things are at. That said she just messaged me before and let me know she would get back to me about when she is free to hang out.