I would never presume to define for anyone that "perfect" length of time before saying "I do". Only you and he can decide that.
However, that being said, packing up and moving to another country, especially with kids, is as Mindy said -- a major, major change. You are basically giving up all you've ever known and jumping into the unknown. For some it can be an amazing life change, for others it's been a nightmare (the cultural adjustments, depression, the missing of family, etc). All the more reason to be as positive as you can be that this person is the right one for you.
I also met my husband online so I can understand what you are going through; however, for us the connection wasn't instant. It took us a little longer to realise that we were right for each other.
He asked me to marry him right around Christmas time. After I said yes, it took about two weeks before I finally realised all that it would entail to marry him and move to England. The visas, the movers, the flights, the wedding, legal wrangling with my child's father over taking him out of the country, the difference in school systems, etc. But do you know what finally made me realise just what I was giving up? I sat in my living room, looking at my artificial Christmas tree, knowing that I couldn't take it with me and just burst into tears (and I'm not a weepy person!). I know it sounds stupid to cry over an artificial tree and the loss of the tree certainly didn't change my mind, but it's the little things like this that can make moves very heart-wrenching. Again, all the more reason to be as positive as you can be that this person is the right one for you.
My best advice to you is to spend as much time with him in person as you possibly can. See how he interacts with your children. Try to make at least one trip to the UK and whilst you are here, don't do the touristy thing. Instead, do the every-day-life thing. Go grocery shopping, learn to get about on your own or on public transport, cook meals, visit schools, watch the news -- prepare yourself for the business of normal life. This is the one thing I didn't do and one reason why I feel I was so ill-prepared for the differences between our countries.
Above all, read as much of this forum as you can. Whilst your future husband can tell you the differences between the UK and the US, actually reading how those differences have affected expats can be a real eye-opener and will help to prepare you for your new life. I certainly wish I had found a place like this six years ago because it would have made me better able to cope with the adjustments.
Good luck and welcome to UKY.