NetherlanLet's look at Denmark and it's potential
Modern Denmark without oversea territories are roughly 43000 km2, it have a population 5,8 million and a population density of around 136 people per km2.
In 1814 the Danish core also included Schleswig-Holstein, which are roughtly 16000 km2, which have a population of 2,9 million and a population density of 182 per km2
Altona (270.000) and Eimsbüttel (260.000) districts of Hamburg was a also part of the Danish kingdom.
Danish oversea territories was
Greenland: 55.000
Faroe Islands: 49.000
Iceland: 340.000
United States Virgin Islands: 105.000
Part of Ghana (population of the controlled parts unknown)
Tranquebar India: 23.000
Serampore: 180.000
Nicobars Islands: 37.000
Danish was historical mainly a agricultural produce and even today it's a majo agriclutural producer, it produce enough food to feed several times it own population.
Mining in Denmark are mainly bulk materials like clay, chalk and sand, it have a very limited potential as a coal, lignite and peat producer. By moder day it have a medium sized extraction of oil and gas production (enough oil to cover domestic use and more than enough gas to export it) and it's believed that there's a significant potential for fracking.
Denmark have one thing going for it in the 19th century, even with the very limited reserve of fuel and lack of metals, Denmark was able to industrialise thanks to almost all major towns having access to sea, the few exceptions had access to small navigational rivers. As such Denmark already had a a transport network before the railroads.
Danish early railroad network
Geographic the Danish island and the east coast Jutish peninsula was very productive agricultural regions. But the western part of the Jutish peninsula was dominated by a massive heath in northern Jutland and by marshland in the duchies. When Denmark lost Schleswig-Holstein it was able to expand the agricultural area with a areas bigger than the duchies by putting the heath under plough. Eastern Schleswig-Holstein and the islands of Lolland-Falster was the most fertile parts of Denmark. The southern coast of Holstein was the main center of Danish industrialisation until the loss of the duchies after which those industries fell into decay, as they lost access to their old markets and Prussian import-export policies worked against te industrialisation of these regions. Schleswig-Holstein still suffer under this and are the poorest West German state.
So now that i have covered the basic part of Danish weaknesses and strenght. Let look at what we could do in Europe, if Denmark could increase the population density to the same as Schleswig-Holstein's, Denmark in its modern border would have around 8 million people, when we includes the duchies the population would lie around 10 million people. Not impressive but a improvement.
I think the first problem we have to deal with is the Succession Crisis and Schleswig Wars. These problems could be dealt with together. We could go several ways, the easiest way would be that Frederik VII produced a heir, he doesn't seem to have been infertile, or that his father prouced another son in his second marriage or that his uncle produce a son. To deal with the Schleswig Wars let Christian VIII live a little longer, as he would be unlikely to surrender completely to the 1848 uprising as his son did. A slightly more conservative government in Copenhagen would have lead to the duchies not rebelling. There would still be unrest, but without the 1st Schlewig War and the Succession Crisis, Denmark would pretty much have stayed a Scandinavian-German version of Belgium. With Holstein being the industrial part, while the more rural Denmark supplied material and labour to the growing industry in Holstein.
Denmark not being busy with national feuding and dealling with a decade long succession crisis could also focus resources elsewhere. It could begin a earlier colonisation of the heath and marsh. It could invest greater development of Iceland and Greenland, especailly because it would have greater capital. Iceland are pretty marginal, but agriculture could have been expanded there. Greenland have a greater potential for mines.
As for colonies elsewhere, it demand a slighly more visionary policy from the Danish government. But it would make sense for Denmark to see if it could trade Tranquebar and Serampore for the British forst in Ghana and Nicobars plus a large sum of money for the Dutch parts. This would pretty much give Denmark control over Ghana and Togo, which would give raw material to its industries. Denmark had already done a lot to expand the local farms. Later as Denmark had success in expansion her, we could see other colonial projects, like going for Namibia-Botswana, and maybe getting the foot in some other before the colonial race really begins. The problems are that the real good real estate is already taken or able to defend itself against a minor international actor like Denmark.