If you're calculating population growth rates keep in mind that the rate of birth and maturation is only one possible positive.
Dwarves have a distinct advantage in that, according to the age chart in the PHB, they have the longest life span in terms of generational cycles.
A human being might live through three or four generations.
Elves live through, if memory serves, two or three.
Dwarves live through something between four and six. I also recall that they have phenomenally long periods of fertility.
Essentially, dwarves can pull off the sucessful businessman thing and raise two or three sets of kids to maturity before they loose all ability to have kids.
Combine that with a high constitution that enables them to age particularly well.
And even though an individual family of dwarves, in the nuclear sense, might take forever to grow as opposed to say a good human family, particularly one that belonged to a good patriarchal culture with Old Testament style family values, the dwarven nation as a whole is going to increase in population at a very good clip and have an extremely robust population of talented individuals.
Essentially, dwarves would have a late developing nation demographic with a huge population of elders, young adults, and mature individuals. One that would be all out of proportion to the number of kids.
Unlike, say, the US, however, that huge population of elders would still be a very productive force within the economy.
So, the only way you'd come up with the dying breed hypothesis from Tolkien is if Dwarves had a really poor gender ratio or young dwarves kept going off on adventures to die since all the great jobs at home were held by elder dwarves who refused to retire.