A wise Mner told me, when I had basically the same dilemma of kids, no time, etc... (though different circumstances leading up to it) that once one has had kids or are a bit older, there are always going to be complications. So, eventually, if you don't want to remain single, you'll need to take the risk of investing time and emotional capital in a relationship.
On a practical level - your DD is 4, so at school, or soon will be? Would daytime dates ever work while she's there - lunch or a coffee? We did a lot of that, as my evenings were too busy to get together a lot then.
Or you could try to find a friend to do babysitting swapsies with?
In some ways I think it was good for our relationship, that arrangements had to always fit around my childcare plans (and work, and housework, and the dog..) - it meant he got to understand the realty of my life really quickly. If he hadn't been keen on fitting in, or had taken it personally when I had to cancel dates at short notice, then I'd have been able to weed him or quickly.
On the costs... very quickly we went to taking it in turns to pay. When it was my turn I would cook, or pack up a picnic. When it was his, sometimes we'd go somewhere expensive. Having said that, if he regularly spent £200 on a night out I'd probably have concluded that we weren't a good long-term fit for each other, but as we had just as much time when we stayed in and played scrabble (not a euphemism 
) it didn't bother me what we did - we had fun whatever.
Whatever you decide, good luck. 