Hello I am Dr. Joey. Thanks for trusting me to help you and your pet today. I am a licensed veterinarian with over 15 years of experience. I look forward to working with you.
Ham is incredibly high in salt and can lead to profound dehydration, especially when in combination with diabetes mellitus. It also is high fat, which could make her a bit unregulated with her diabetes.
If she is having any vomiting, refusal to eat or continues to be very lethargic beyond 6-8 hours, then she really must be seen by her veterinarian. She may be incredibly dehydrated to the point she needs IV fluid therapy. I have actually seen salt toxicity occur in a dog which ate too much ham. In Jess' case it sounds like she only ate the bone, which may be slightly less salty than eating the ham, itself. But salt toxicity can be deadly in a dog. All the electrolytes get way off balance and it leads to brain swelling. This is why if she is becoming progressively more lethargic, she must be seen immediately by either your closest emergency veterinarian or your regular veterinarian, if open.
If she needs treats, then you do need to be cautious. I would stick with a "light" dog biscuit such as one made by Hill's (their hypoallergenic treat is good). Or you can use carrots or other pieces of small fruit (no grapes, onions, macademia nuts, garlic or avacado).
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