To analyze transgenic plants, we have to detect zygosity and copy number of plant. It should be considered that we need it just for nuclear-engineered transformants.
Southern blot is a standard way to assess zygosity in mammals by using a densitometer to read bands. If your plants are diploid, Southern blot can be used confidently to assess zygosity. However, bear in mind that with higher numbers of copies of a sequence (e.g. triploid, tetraploid and so on) it will be more difficult to establish with certainty the copy number, i.e. telling 1 copy from 2 copies is easy, telling 6 copies from 5 is not so easy.
I have used Southern blot only for assesing copy number in T1 plants, so I'm not quite sure of its usefulness for analyzing zygosity. I think PCR methods are more useful and reliable for that, since standarization is easier than in Southern blot:
During my PhD, I had to quantify the copy number variation of certain endogenous retroviruses in the genome of domestic sheep. In order to do so, I performed qPCR assays and normalized the values obtained with a housekeeping gene and two other endogenous retroviruses. I think you could apply the same technique to quantify the copy number variation in your transgenic plants.
Concerning the heterozigosity instead, I think that by analyzing the segregation of your plants in one generation, you can understand whether the parental line was homo or heterozygote.
You need to include a standard diploid lane to "normalize" your samples and then you refer all other bands to this standard. This is commonly done when assessing the number of insertions of a transgene in the mouse genome - as you choose the enzymes for the Southern blot digestion, you can have just a single band of your probe per insertion in your blot. Then, you can tell because of the intensity of each band and its location within the lane how many insertions you indeed have (two insertions mapping very closely in the lane give a higher intensity band).
If I recall correctly, this is discussed in chapters 1 and 6 of the "Molecular cloning" handbook by Sambrook and Maniatis, and also in the book "Molecular Biology Problem Solver". You can see an example of this technique in my publication NEJM 2002; 346:243. Good luck.