Mamadouba is dead right about the need to understand the landscape & the rate of change. Also, you need to be aware of what NDVI actually measures. The following points apply:
1. NDVI or a similar index (they all have pluses & minuses) will tell you something about how green vegetation changes. It is not a good indicator of dry vegetation.Thus, after rain, you will get a strong NDVI signal but after green vegetation dries off, it becomes yellow, brown or grey & your NDVI signal drops off, even though you may have exactly the same amount of ground cover by plants. Essentially, all that happens is that you are swapping green biomass for dry biomass. This is not desertification. Also, a strong NDVI signal may indicate encroachment by woody shrubs at the expense of herbage. In some parts of the world, this is a form of land degradation.
2. NDVI varies in response to rainfall. If your rainfall varies seasonally, you will need to filter out the wet/dry season variation & to extract a longer term trend over time. This will require a time series of data. If your rainfall is variable over longer periods (i.e. subject to ENSO generated wet & dry periods), that will give you substantial NDVI variation over time. Again, to detect true desertification (i.e. loss of the ability of a landscape to produce plant biomass from rainfall), as opposed to short term drought, you will need to filter out the effects of rainfall variability. Hence, the need for a long time series of whatever index you plan to use. The length of the time series needed will depend on the amount of rainfall variability in your environment.
3. Desertification is a term that means different things to different people. I have seen it widely misused & frequently confused with changes in vegetation cover associated with long term changes in rainfall (i.e. confused with the effects of drought). I think what you are after is a loss of landscape resilience, i.e. a capacity to bounce back from imposed stresses, be they natural or man-made. When you develop your methods of analysing a time series of satellite data, you need to show that loss of landscape resilience can be proven. Almost certainly, this will require a long time series of data which forces you to use Landsat or AVHRR. There are exceptions but these are restricted to situations where you have rapid & extreme land degradation.
4. There is loads of this stuff in the literature. Australian researchers probably produced the best developed methods for separating land degradation from rainfall variability & drought using both time series & spatial patterns in remotely sensed data.