Most single parents are expected to find work when their youngest child reaches school age and so aren't entitled to income support any more. So yes there are plenty of single parents who work.
I appreciate wanting to go back to work, but why do you want to be full time? Unless you are on very good money you'd still get some benefits. And you might find the difference between that and working slightly fewer hours, or even part time, is marginal overall.
As a single parent, you get WTC if you work more than 16 hours a week. The amount you get reduces the more you earn, but you get an extra boost if you work 30 hours per week. You also get help with childcare costs but there is a weekly cap. It may not cover all your childcare costs if you work full time. You should look at the entitledto website amd also look at your local childcare and see what they actually charge.
Also what are you planning to do when your dd starts school? You may find it easier to attend school events and to do pick up and drop off yourself if you work part time. Unless you have lots of family support for school runs you'll be looking for school clubs and child minders to do that for you. You also have to have child care in place for all the holidays, inset days, snow days etc.
My Ds is now 16 and I've been working 30 hours a week term time only for the last 4 years. When I first went back to work (he was 5) I did 18 hours (3 days x6 hours including school holidays - I would work extra days in term time to have half terms off time in lieu, and used holiday clubs for the summer plus easter and annual leave for xmas).
With little family support I always made sure I was there for school events (sports day, class assembly, open afternoon, fetes etc). With just one parent ds needed that, and I wanted to be there for him too. Working 3 days meant it was easy to swap which day I worked to be there for such things. I was lucky to find a very flexible employer though.
As his needs have changed I've upped my hours. It's not been easy but it means I have a foot on the ladder and when he finishes school completely I'll be able to work more hours again. I'm still with the same employer 10 yers down the line. They know I'm hard working and will make up my hours and be there when they need me at the busy times of year. Depending on what work you are hoping to return too, you may or may not find your employer is or can be flexible like mine is.