Hello JW,
I suppose that your AD model induces brain atrophy instead of hypertrophy.
The main missing point that I see from here is that you missed to run a DARTEL normalization step on your data.

Indeed, the normalization step provided in the previous batch is a linear (X/Y/Z + shearing) and you have to perform a non-linear normalization before compare your dataset.
This step is quite long but it permit to calculate the jacobian fields (u_files, please see SPM doc) to warp your GM correctly.
The warpped GM images should be used to perform VBM.

Please have a look on the following papers for details and examples of VBM procedure in rats:

Regional gray matter volume increases following 7days of voluntary wheel running exercise: a longitudinal VBM study in rats.
Sumiyoshi A, Taki Y, Nonaka H, Takeuchi H, Kawashima R.

Voxel-based morphometry and histological analysis for evaluating hippocampal damage in a rat model of cardiopulmonary resuscitation.
Suzuki H, Sumiyoshi A, Taki Y, Matsumoto Y, Fukumoto Y, Kawashima R, Shimokawa H.

Structural and functional alterations in the retrosplenial cortex following neuropathic pain.
Barrière DA, Hamieh AM, Magalhães R, Traoré A, Barbier J, Bonny JM, Ardid D, Busserolles J, Mériaux S, Marchand F.

The SIGMA rat brain templates and atlases for multimodal MRI data analysis and visualization.
Barrière DA, Magalhães R, Novais A, Marques P, Selingue E, Geffroy F, Marques F, Cerqueira J, Sousa JC, Boumezbeur F, Bottlaender M, Jay TM, Cachia A, Sousa N, Mériaux S.

Otherwize, your comparison sounds good, nevertheless I recommand you to calculate the volume of each brain. To do that you could binarized and sum your GM and WM maps (released during the segmentation step(in native space)) in order to calculate the volume of brain parenchyma. Then, you could used the brain volume as regressor to limit the group effect in your analyse.

Finally, you should keep as default the Global calculation/Global normalization and Grand mean scaled value. I think is recommanded for PET analysis but not for MRI.

Good luck.

David from the SIGMA Team