I would recommend looking at pre-existing numerical models, rather than computing your own. This has a couple of advantages:
- You don't need to use any approximations.
- Factors like metallicity, rotation and composition have already been taken into account.
- You just need to look up the values in a table - no calculations required.
- You can also compare values for a star of the same mass and composition at many points in its life cycle.
I usually point people towards the Geneva grids of stellar models. They're easily accessible and simple to use. Let's say you want to look at stars of approximate solar composition ($X\approx0.76$, $Y\approx0.24$). There's a set of models by Schaller et al. 1992 that should suit your purposes. You probably want Table 43, for $M=0.9M_{\odot}$ - close enough to your star's mass. If you look at the column labels, you can see that Column 2 gives the star's age, in years, and Column 4 gives the logarithm of the star's luminosity, in solar luminosities.
I took the liberty of plotting luminosity against age for this particular model:
Notice the steep increase in luminosity at around $\sim10^{10}$ years, when the star leaves the main sequence and enters the red giant phase. Additionally, I calculated the boundaries of the habitable zone. I assumed that the inner edge corresponds to an effective temperature at 273 K, and that the outer edge corresponds to an effective temperature of 373 K - the freezing and boiling points of water.
If you play around a bit and check out different grids of models, you'll indeed see that factors like mass, metallicity and composition strongly affect the evolution of a star, which is why it's important to have fine enough grids of models in the first place.
