OK I am going to try again in case OP returns because my post above might have got lost in the bunfight.
I suggested that the sensible thing to do would be for the OP to sit down with OH and look at their own budget and see whether they can afford to have a child, and what the financial impact would be.
I would also add that in the OP it says:
I ask because my partner is paying his ex over the odds in maintenance because he thinks she is getting next to nothing. However, a friend of mine says his ex gets more money than him due to the amount of benefit she receives.
So it isn't the OH who is questioning the amount paid, it's the OP, on the basis of what a "friend" of hers has said.
Why would the OH "think" she is getting next to nothing, if that wasn't the case?
She is on benefits - she will be getting the bare minimum, and that will reduce over time as prices are going up higher than the 1% cap.
You can try to calculate the benefit she receives here.
She has a mortgage, so she won't qualify for housing benefit. The most help she will get with her housing is SMI - mortgage interest support. So that is help with the interest, not the mortgage repayment. That is paid direct to the lender, so she won't see a penny of it.
As for child maintenance, you can make a rough calculation here of what your OH would be paying if he were to withdraw all other support. Frankly unless your OH is being exceptionally generous I doubt whether it will make much difference to your budget - however it will no doubt make a huge difference to hers. Therefore if you care about your SD, as you say you do, would you really want that to happen?
Your suggestion that if she would allow it, your OH having more contact with the child would lead to a reduction in her costs is rather wide of the mark. It will make no difference to her fixed costs in relation to housing and utilities, which make up the biggest proportion of her budget.
I think if your OH is so concerned about being misled by his ex he should raise it with her. However, if she is on benefits and trying to pay a mortgage, I can guarantee you she won't be "more money than him".
You may feel it's your business because you live with your OH, share living costs and are planning a family. But his relations with his ex are not really your business, they are his responsibility to maintain.
I think you'd be very unwise to have any discussion with your OH about this on any basis other than your own joint budget.