I also had a short courtship "in person" with the man who is now my hubby. We originally met online and chatted by internet and phone for 5 months and then met in person after which only 4 months passed and I moved halfway across the country with my 5 yr old daughter to be with him. We were legally married in a courthouse 5 months later and then planned an actual "wedding" 8 months after that.
I will say, after having been through abusive relationships and realationships where I found myself compromising to the point of "settling"-- when it's right, it's just right. But if there is a seed of doubt or red flags, then it's time to reconsider. But we're all adults here, and I will go forward with my advice based on the fact that it obviously seems right to you. :)
Let them have time together to bond. Maybe they can start a fun new routine together just the two of them. Can he take her to the park every Saturday or make pancakes together on Sunday? Could he help her learn to count and do math? Etc, etc. Maybe the two of them have an interest in something like computer games that you don't have... let them bond over those things.
When we planned my wedding, we planned it as a family joining. My daughter was the flower girl, but after our vows to one another as a couple, she joined us in the middle and we made vows to her and she to us (she simply said that she promised to love and respect us both as parents) and we lit a unity candle with 3 candles instead of 2, we had a group hug and then all recessed together. She even registered for a few small gifts (like a lamp for her room, a purple flashlight, a pretty throw pillow, etc) We made the reception very family-oriented and made sure we included her in the tastings for food, etc. so that she would be a partner in the whole party. She LOVED it.
I do think it's better for them when they don't know their biological dad (my daughter doesn't either) in that they do bond quicker with other males in our lives. That can be a huge drawback if things don't work out (I've been through that with her in my dating stage) but it's wonderful when you do meet a partner who is willing to be a loving parent.
I can tell you that we are all very happy. We have been married for a year and are expecting a new addition to our family in November. My daughter has moved across the country, been in 2 (soon to be 3) new schools, lived in 3 homes in the past 2 yrs, left family she loves and met new family she loves, been exposed to a different culture, new friends, new routines, etc. and she is still emotionally healthy and resiliant to all the change. If you love your child and that is unconditional- they will know that and be just fine. Children are strong, but we must be strong for them as well. Put her first and all else will fall into place.
Best of wishes,