Yes, decent men date single mothers. However, I think it's probably a bit too soon for you.
Dating is a potential minefield of crossed wires and rejection at the best of times. If your self-esteem is already a bit low, best to work on improving it. That's best achieved as a single person - self worth can never be achieved from validation through the eyes of others.
Also, I know from when my DC were that young (I was a single parent of DTs from when they were 4 months old), that it would have been difficult to fit in time to really start a new relationship. Take out work, running a home and my DC, there was precious little 'me time' available, let alone time to fit in a relationship. If you sacrifice me time for a relationship, you really heighten the risk of picking a partner who will turn out to be manipulative/abusive/just plain selfish as you've already set the parameters - I count less than us.
I spent 6 years as a single parent. During that time I really concentrated on my bond with my DC, developing myself and developing my friendships (many with other single mothers). Despite the lack of funds in the early years (which really was horrific at some points), I look back on those years with extreme fondness. My self esteem grew hugely as I realised I could make it on my own and TBH it was the making of me, leading to a career change and vastly improved prospects. I then met my current DP who has turned out to be a fantastic step father.
I echo those saying take it slowly if you do meet someone. As a single parent, it is easy to fall into the trap of having dates at home and mixing in the kids to activities with your new partner. Money is tight, child care difficult to arrange, and it seems to combine the best of both worlds. IMO however, it's a mistake.
I think it's a good idea to introduce new partner and DC quite quickly (no sense in developing a good relationship only to then find he and your DC hate each other), but keep it light and uninvolved so he's only ever someone on the periphery for quite some time. And increase his involvement slowly. I took longer than most and each family is different, but the timescale I had was 6 months dating before being introduced (we only had 1 or 2 dates per month due to us both having busy lives). First introduction was a fun, family day out in which he also came along. No pressure on anyone then to bond. Then he'd pop in for a coffee before we'd go out on a date. This went on for about a year before he first stayed the night, and during that time we built from coffee to him staying for an evening watching a DVD with us before leaving.
The second year he became more involved in their lives, helping with homework, attending events with them, family days out together, etc.
The third year, I finally allowed him to read a bed time story with them and put them to bed. Not because I didn't trust him to do that before then, but because that time with my DC is sacrosanct (as it is for most children) - one time when they have my exclusive attention, the lights are low and they can confess any fears, etc. I needed to be sure that they were ready to 'lose' that time with me because they felt here was another adult who they could trust and turn to if they needed help.
Year four, he moved in.
DP now parents 50/50 with me, more so than many biological fathers (sad indictment on society). Parents evenings, days off when kids are sick, etc. He will take on primary care if I die.
It can, and does happen, that decent men date single parents. As a single mother, however, you have a duty to yourself, as well as your child, to ensure you are in a position where a relationship will enhance your life rather than become something else to juggle, and you need to be able to recognise those red flags and walk away if it's not right.
Good luck. 