Technically, due to is used to modify nouns and because of is used to modify verbs. To be honest both would be understood as the causal factor driving up the population.

Some grammar experts would say that “due to” is wrong in that sentence, since “due” is supposedly an adjective, and therefore must modify a noun. A correct sentence would be “The ballooning (gerund)of the population of African meerkats to an unprecedented high was (main verb) due to a lack of predators in the area.” That said, most native speakers would probably not have a problem with the original sentence as written. I cannot imagine that there aren’t dozens of more important grammar points for you to be learning now.

The sentence is perfectly understandable. Good job. (What do meerkats taste like? Maybe people could eat them.)