I am an ex-single Mum I dated guys solely from online, most successfully (and safely) from RSVP, till I met my husband. I totally recommend online dating, but be sensible, take it slow, meet in very public places, keep details about yourself private (address, workplace etc) and enjoy!
As for finding the time to actually meet, I actually met up with my husband (after having been introduced by a friend and chatting on FB for a couple weeks) for 45 minutes while my daughter was at her school disco! We met at a bar nearby, I had time to drink half a glass of wine then had to dash off!
Can you ask a friend to mind your little one for an hour while you meet for coffee maybe?
dating as a single mum is certainly incredibly difficult and different to the alternative. I actually managed to date really good men though. I was always upfront and honest about my daughter (who I have 100% time) and very strict with who I spoke to, let alone met up with, and it seemed to weed out the weirdos.
good luck, there's hope on the other side. I'm now 3 months married and 3 months pregnant with my second, his first, to a wonderful man who has taken my daughter on as his own, and is now her Dad