At the time, Denmark and Sweden was at each other's throats over dominion of the Baltic (with Sweden slowly getting the upper hand), I don't think a union would be possible at the time. The Swedish nobility would probably demand that Kristina abdicate if she was to marry a Dane, or at least that their children were not in line of succession, which kind of defeats the whole thing.
Besides, Kristina was raised as a boy would have been and quite strong-willed. She showed no real interest in men (there's still some debate on wether she was a lesbian, bisexual or perhaps had an hormonal disbalance), at least not the man she was supposed to marry, her cousin (that would later become Karl X Gustav). Some of her letters to Ebba Sparre hold a distinct erotic tone.
Regardless, Kristina was very strong-willed and decided early not to marry. Her mother was mostly hysteric and her father dead, so there was no-one to force her to do anything really. You need to have Gustav II Adolf survive and force that marriage for it to happen, methinks. But if he lives, why would he marry his daughter of to the Danes? He did not really like them. If he had lived, he could perhaps have had a son too, and then it is possible, but then Kristina is not the heir to the Swedish throne anymore, and the idea of a union falls again.