tulipbulbs - "there's a lot of love in a no" - this is very true!
Op - are you rushing because you want to replace the baby you lost? This won't replace that one, it'll be it's own person, and it's own person whenever it arrives.
I'd say you can cope if you do it now, but in 3-4 years time you could be in a position to do better than just cope. You are in a rented property, so could be given notice in 2 months, read some of the threads on here with the difficulty of renting when you have children. Right now, 2 full time working young adults, you are a landlords dream, stable incomes, minimal wear and tear on property. Small child makes many landlords wary. If you can live with a grand a month less (full time nursery place), then you could save that now and in 2 years have £24k deposit (or more if you can make other sacrifices to save more) to buy. Once you have dcs, you'll never have the same disposable income to save unless one of you takes a massive step up career wise, and that will be harder to do if you can't do extra study, or put in longer hours at work as you have caring responsibilities.
Waiting 2 years would also mean you have many more rights at work, your DP can recover more and look at increasing income and possibly plan a small wedding - as pp said, if you/he shies away from marriage (for none political reasons) then perhaps your relationship isn't for the long term, best to avoid doing something that ties you together.
The average age for a first time mother is much closer to 30 now, society is much more set up towards spending your 20's getting settled before having dcs, while it's possible to do after having dcs, it's much harder to do - I can see why your mum doesn't want you to make your life harder than it needs to be.