My exh left before my dc was born, so I did single parenting right from the start. My first piece of advice is to get your practical support network organised so you can get back to work, as you need to build your own future. The first few years are tough - children pick up every bug going in nursery, it's exhausting doing everything and it's hard to watch friends who have partners get help (and have homes with 2 incomes when you only have 1), so get your plan B sorted so you know you can get through the day if something doesn't quite go to plan. I had parents in the next town and a couple of incredible friends who helped in emergencies, so I bought a spare car seat to leave at nursery, for example.
Next, don't panic! I was living month to month financially at first (I have a secure but not high-paying job), but I budgeted carefully and got into a routine. Again, the first few years were tough as I saw friends have holidays, go spur of the moment shopping etc. when I couldn't, but slowly things got easier as I built my financial foundation. By the time my dc started school, I had a little bit of a buffer behind me that I made sure I hung on to.
Don't worry about being on your own forever. I had relationships so having a dc didn't put people off. Dating is harder than when you don't have children as you need to sort a babysitter, but it's do-able. I always made sure to keep my finances separate though, so if things didn't work out, I knew I could provide for my dc and we'd be ok.
Fast forward 20 years, and I'm married - to someone I'd known a long time but never thought of romantically until one day, there he was! He also has dcs (similar age to mine) and we consciously decided to properly combine homes, finances, everything. Our DCs are OURS. Yes, the genetics are different, but we both parent them all as if they are ours. The DCs know their home is with us and we share the roles - he might give my dc a lift; I might take his to the dentist, whatever. It works well and I am very happy, but I look back on my time as a single mum in my own little house with my dc with real happiness and affection. My dh is fabulous, but it was a wrench giving up the life I'd built for myself, and I wouldn't have done it for a lesser man.
So build your future now. Build your financial security and hold on to it whilst your dc are dependent on you. That way, if you do decide to commit to someone again, it will only be because you really want to and you know they are worth it, not because you need to or it seems like it would be easier. And don't compare yourself to others along the way - sometimes you'll feel 'behind', but no-one knows what the future holds and just because someone else looks like they have it all, it doesn't mean they will still have it all in 5 years time.
Oh, and enjoy the little things and find someone to take some photos of you and your little one so you have some with you in to look back at!