Getting divorced is also one of the most stressful things you can do in life. You need to be kind to yourself as it's going to take a toll on you mentally.
It isn't ideal to be taking on an unfamiliar new job/colleagues/workplace, with all the resulting training and finding your feet that you'll be doing, at the same time as:
Adjusting to moving from part time to full time hours and having to completely alter your routine.
Becoming a single parent, which you might feel you already are, but even a useless DH is physically there in the home with a sleeping DC while you pop to the shop etc. Once you've got DC totally on your own life is so much harder to get things done.
Dealing with the emotional fallout of the divorce, you're probably numb at the moment and you haven't yet discovered the almost inevitable presence of the OW waiting in the wings. At some point you're likely to have a lot of difficult feelings kick in and you'll need time and space to process them which is difficult to find when you're single parent to a young DC.
Missing DC when he's not with you and having to accept your ex's ways of doing things with DC when he has him, can take an emotional toll too. Co-parenting can be really stressful.
Dealing with the practicalities of divorce, which may get nasty. He's only Mr Trying To Appear To Be Reasonable now because he thinks you'll cave and do what he wants. When he realises that divorcing you loses him your loyalty and compliance, he won't be happy and an unhappy man doesn't generally look at all reasonable, they generally look like sulking or tantruming toddlers.
IMO new job is added stress you just don't need right now, if it can be avoided.
When DC goes to school having to juggle full time hours with school pick ups, inset days, DC sickness, etc it's not easy unless you're earning enough for paid help. It's the kind of new challenge to take on when the dust has settled from everything else, you can see what your new circumstances are and look to improve them if you're unhappy. You'll also be in a better decision to decide what direction to go in instead of scrabbling around in a panic and possibly getting stuck in a situation that doesn't work for you and a job that causes you endless stress in itself. If you hate your current employer and they're toxic perhaps this is less of an issue, but if you're happy where you are now don't be in a hurry to give it up.
Don't worry about what STBXH wants just do whatever is best for you and DC. Money isn't everything, once you've got the basics the biggest issue is rent/home repairs if owning, so adjusting to being skint is possibly going to be a big change for you to get used to (depending on your earnings capacity). Being skint and topped up by UC isn't necessarily all that different to working more hours and not being topped up by UC, but having a bigger struggle to fit everything in. There's also housing costs element of UC if you're renting, that you don't get if you own. Working more isn't necessarily going to buy you a better standard of living, it depends on your earnings potential whether it does or not.
So don't bust a gut chasing a dream that someone else has laid out for you. Take stock of your own life in your own time and make your own decisions to suit you. If STBXH has an issue with you renting, working PT and being on benefits then perhaps he shouldn't be divorcing you! If he looks bad to his peers, or feels guilty, or is snobbishly ashamed for DC etc, because you look broke, that's not something for you to GAF about.