NTA. It’s okay for you to ask, her response was totally out out of line.
Idk what part of the UK you’re in so laws may vary but if she doesn’t move her baby to another room you can take this case to a local council, and if they find evidence of a noise violation they may be able to issue an abatement which would require her to put her baby in another part of the house during hours that you’re working.
The fact that she screamed at you when you requested mediation may work in your favor as the UK doesn’t usually investigate noise complaints unless the neighbor exhibits behaviors like harassment.
Here’s a link with more info on steps to take so you can reasonably work from home and continue to enjoy your property without the continuous noise of a baby. While likely not controllable at all times, I think what you’ve described really does impact your day to day in an unreasonable way and deserves further investigation by either the landlord who can add sound proofing or a local council.