@Partygirl2021 I lived in Dubai for most of my adult life and whether you can afford to live there is really a matter of your standard of living and expectations.
DH and I lived on less than your salary with no expat package at the height of the most expensive time, but it was hard - we lived in a (very nice and large) one bed flat in Mirdif, had one car (bought outright) and budgeted pretty tightly. DH had been made redundant so we managed for 9 months but it wouldn't have been sustainable long term. The trickiest thing finance wise will be education - good international schools aren't cheap (check out the fees for schools like Victory Heights, JESS, DESS, GEMS Jumeirah Primary, Arcadia, Sunmarke, Southview for an idea of average fees).
The days of generous expat packages including education and housing allowances are rapidly disappearing and have been doing for sometime now.
On the other hand, rents have come down massively in the last 12 months. You can now rent a 3 bed townhouse/villa for the same price we were paying for the 1 bed apartment I mentioned. If you don't mind being in a residential area (eg. Springs/Mudon/Remraam/shorooq/Al Waha/meydan/akoya to name just a few small areas) rather than the heart of the city/marina/downtown then there are affordable options and you'll find a live in maid affordable which can be a blessing as a single parent.
Contrary to many people's assertions above, you don't actually need an employers sponsorship anymore to get a visa. Dubai launched a remote worker visa in October last year and you can now get a residence visa as long as you can prove an income of $5000/month and have adequate health insurance. So if your employer is happy for you to work remotely from there you could simply go with evidence of your payslips.
Dubai is what you make it, if you want to go and live in a penthouse in the marina and be able to go for brunches every weekend and drive the latest Range Rover then you'll find it expensive and likely unsustainable. If you simply want a change from your life here and are willing to compromise and live as a normal person, socializing with all nationalities in a variety of places from fancy hotels to hole in the wall restaurants, you can live quite easily.
Life as a single mum is arguably easier as you should be able to afford live in help and much of Dubai is set up to be very female friendly (you can usually skip queues and have separate, quicker offices for government business) and children are welcomed most places. I've never felt safer in my life, in fact I regularly feel intimidated/ afraid here in the UK whereas I could happily go out by myself at 3am in Dubai and feel perfectly safe.
It can be very hard with a young child at the height of summer as the what means paying for expensive indoor activities like soft play etc just for them to burn some energy and many mothers take the kids home over summer to escape the heat and visit family - if you are the main breadwinner you obviously can't just take off for two months (unless you can work remotely) and this can be hard but it's really only June- September that it's really hot. Otherwise, it's pleasant and you can have pool time everyday for free, so you'll likely have a waterbaby on your hands!
Basically, as with anywhere, any overseas move will largely be what you make of it. I've lived in 4 countries and there have been pros and cons to all of them. Do your sums first (check out dubizzle.com to get an idea of the cost of big things like houses/cars) and if the maths works, as others have said, take a holiday there, see if you like it and if you do, give it a go!