Hiya. I was a single dad at 28 with a child of 5 and a 1yr old baby. So I totally understand where you are coming from.
Back then a lot of "eligible" ladies did not have kids themselves so were not interested in taking on "baggage". Frustratingly a few single mum's turned me down on the basis that they wanted someone without a child too. It would seem that I was doomed.
Unlike you I did manage to hold down a job thanks to a really understanding employer but after mortgage/childcare etc I was flat broke every month. Literally. My ex paid nothing. For some time I didnt even dare go for child benefit in case it triggered her to go for custody. Something which was not in the children's interests.
I did get a few dates and eventually found a young single mum of two like myself and we ended lived together for a few years.
I became single again just under two years ago. By then I'd established my career so financially better off. Being a bit older meant the ladies nearer my age were more understanding of a single parent. Without meaning to sound big headed, getting a date was WAY easier.
I found that most women had grown tired of the exciting bad guy who would shag/drink & gamble and instead were looking for the nice guy who would look after them and be a good provider. So if you can sort out a decent job (or prospects) you are all set as you already get a tick for being a good parent (not many dad's would take on their kids full time).
The thing I will say though is this. Look at jobs in the longer term. As I mentioned when I first started, there was nothing left. Nothing. In fact I would probably have been better off either going PT or even going onto benefits. But I persisted and took long term view. My kids day started at 6am. They were the first to the childminder/school and the last to leave. The guilt ate away at me. Life wasn't supposed to be like that.
Now though I have a good job, financially stable, we can afford to go on holiday and drive a nice car. The kids don't remember being left at school/childminders all day anymore but now they are older they now do appreciate the nicer things we can enjoy because of the sacrifices we all made.
So my point is (and in all seriousness). Concentrate on building a career. The women will follow.