Rootsireland.ie lookup please?

[Wexflyer]

It may be wise to look at the registers to confirm said dstes. The families are concentrated in Clonmany & Upper Moville so that is where to focus first.

Certainly strange as both NLI and the RootsIreland's own coverage table show Clonmany RC registers not starting till 1852.
They show Clonleigh (Lifford) as the only parish listed as having pre-1835 registers. There will have been Rose Dohertys born elsewhere in Co. Donegal. Some of the surviving Church of Ireland registers are older but many registers are also missing, destroyed 1922. "Held by the Public Record Office in 1919"
https://www.johngrenham.com/records/county_church_full.php?county=Donegal&search_type=full&denomination=Church%20of%20Ireland

With regard to parish register material existing prior to/earlier than reference works suggest, this is not so unusual, for two reasons:

1. Amalgamations and divisions of older parishes. This can lead to register material existing, but in a different later parish.

2. The NLI microfilming effort in the 1970s simply missed many registers. I don't believe there was any effort since to either fill in the missing material, or re-film registers that were so poorly filmed as to be unreadable.

As for CofI records, rather than rely on Grenham, the most comprehensive and accurate listing of extant registers is provided by the CofI itself, at:
https://www.ireland.anglican.org/cmsfiles/pdf/AboutUs/library/ParRegs.pdf

[Wexflyer]

A comment on RootsIreland. I think it is very much to their advantage to show every now and then that they have unique material - which they do.  They must have less than 5% of the name recognition of the international giants, Ancestry and FindMyPast. Any attention for RootsIreland must be to their benefit.

That said, OP clearly is aware of RootsIreland, as the query is specifically for their material. Why he/she simply doesn't sign up for a one-day subscription is beyond me.

[Wexflyer]

Having looked into this, some of the posted Doherty births are not parish register derived (Catholic or Protestant).  Rather, they are associated with with old age pension applications.

[Wexflyer]

Looking further, there is the following note in the RootsIreland listing of online sources for Donegal -
"Donegal Birth Records include Pension applications for Clonmany Parish"

An excellent example of the fact that RootsIreland have access to unique sources that others don't.

Also, given that RootsIreland have one-day subscriptions, I can't see why OP can't invest in one (or longer)?