Every situation is different, but for what it's worth, I spent nearly two years working on the project that would become Littlecat (I like your company name, by the way) before I gave notice at my day job. My approach was to be honest with my colleagues and managers about the fact that I had a side project, and I did admit from time to time that my eventual ambition was to pursue it full time -- but not yet, I assured them, and they would know well in advance when I was preparing to move on. I honored that commitment, giving six weeks notice when I was ready to leave, and working hard to leave on as strong a note as possible. The results of this approach were basically what I had hoped for: my old team was supportive of my ambitions while I was there, and they still are.
On the other hand, I did not create any public profiles stating that I was the founder of a company while I was still employed. I'm not sure whether or not I would have felt comfortable doing so, because at the time I was much more focused on product than on PR and I wasn't really thinking about it.
Good luck with your decision and with your venture -- I hope it works out well.