Mixed-effects models may be explained in multiple ways. In your example, you could think of them as a way of accounting for variance explainable by some categorical variable (such as habitat) without paying the parameter penalty of including the variable as a fixed effect. 

Suppose you had 20 different habitat types. You would have 19 implicit parameters in a regular modelling framework, while in a mixed-effects model you would be accounting for a single variance term (i.e. you would assume that the means of all 20 habitats are drawn from some normal distribution). 

Now to get to the specifics of your case: since you have only 3 habitats, you don't really pay much of a penalty (2 parameters!). And 3 units is a very small number for estimating a variance term in any case. So I actually suggest that you abandon the mixed-effects modelling framework here and include 'habitat' as a fixed effect. This leaves you with a simple linear model:

Length ~ Age * Habitat

A strong interaction term would be clear evidence for your biological hypothesis of growth rate being influenced by habitat, I think. And if you know how to do a regular power analysis, you can go ahead and do this instead of worrying about the complexities of power analysis in mixed models (for which there are methods, e.g. http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12504/full). 

Let me know if this addresses your question; I will try to clarify anything above that isn't clear, or point you towards additional resources.