Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry for this concern for Bonny.
As more testing is done, more breeds are likely to be added to the list of those with the MDR gene. Of the breeds you listed, collies are the only ones currently on that list although that doesn't mean that mixed breeds can't have the gene either.
In terms of your question, the antibiotic that you listed would be safe to give Bonny should she have the gene.
As far as natural remedies go, cranberry has been shown to help acidify the urine and may help to reduce the symptoms associated with a uti but in my experience, antibiotics are the only completely effective treatment once a uti has developed.
Cranberry products may be effective in preventing recurrent episodes, however, for those dogs prone to them.
I'm certain that there are a number of products available on the internet but the following is to a link that I like a lot: http://www.nutramaxlabs.com/dog/dog-urinary-health/crananidin
I hope this helps. Deb