Based on
this table, the population of the Thirteen Colonies was roughly 50 thousand in 1650, which more than doubled within twenty years to almost 112 thousand and in 1700 reached a quarter of a million.
Drakesland had a twenty year head-start on the American Colonies, but is also marred by several factors: distance, arable land being more plentiful in America (though perhaps this is not a common knowledge) and the presence of African diseases. A couple of factors the colony has going for it are the positive advertisement of the colony to the European public and the active attempts to recruit settlers.
I'll try and figure out a population growth rate and work from a figure of 20-25 thousand in 1620, although this rate would likely change from time to time as significant waves of settlers come over (such as migrations of the religiously discriminated - Puritans, Calvinists et all).
Also to take in mind would be the diversion of immigration from North America to South Africa, which would likely be significant in changing the face of the continent as there is a likely chance of many of the Founding Fathers never being born or instead being born in Drakia.
The American colonies had that size in the 1650s thanks to the colossal injection of New England Puritans - 20 thousand in the 1630s. Without something similar for Drakesland they will be
much lower.
Also having anything like the North American growth rate and health is silly, the Afrikaans didn't for a number of reasons ALL of which equally apply to Drakesland
1) The Americans were coming from Northern Europe to an identical climate, all their skills apply 100% rather than having to learn new things in a cliamte that isn't as productive.
2) There were plenty of First Nations around with agricultural skills to crib off.
3) The disease burden in America was virtually nil as there were no native diseases, the Cape is going to catch things from the Africans even out of the malarial zones, and if there is lots of passing trade from Asia they'll get sick from that (several pandemics ripped through the OTL Cape), the New Englander small village economy also helped limit spread, which isn't something the Draka will employ with the trade aspects of their economy.
The southern colonies suffered severely from disease, and South Africa won't be any different.
4) The insect burden is much much lower in the Americas as the Cape doesn't get significant frosts, so you have insect vectors for illness and much less productive farmland and food storage.
5) North America is just a massively more fertile and well watered place than the cape, giving higher calorie returns per unit labour (not that the Draka won't get really rich off trade and mining, but
food will be much more expensive)
20 thousand in 1620 is five times the american colonies at that time, which seems very unlikely.
Given these OTL rates of on year natural increase for the period:
Quebec 2.5%
New England 2%
Appalachians Frontier 2%
Middle Colonies 1.5%
Southern Colonies 1%
Boer Cape 0.5-1%
I think a 1.5% estimate is
very generous and means 20k in 1620 will go to 90k in 1700. Immigration will hike it up but I do think 20k is rather high for 1620. Something more reasonable like 15k will give 45k in 1700.