Lorna it is getting increasingly difficult to find housing that will accept dogs - cats are sometimes easier. Dislike of dogs, while a growing trend in Switzerland, is only part of the problem.
The real issue is that the housing market is tighter than tight - there simply isn't enough housing available for the huge numbers of folks moving to Switzerland, let alone those already here. It's a landlord's market, there are often a dozen or more applicants for every open property. Dog owners represent complications and expense - why rent to someone with a dog when there are plenty of other 'uncomplicated' tennants vying for the flat?
Be aware that as a dog owner you already have one strike against you in the undesireable tennant stakes - so you will need to emphasize your other positive qualities to beat out the competition.
First, consider paying up. There is less competition in the more expensive range.
Second, consider properties that are in poor condition or in undesireable locations - again less competition for these.
Heck, sometimes you find that you have to pay over the odds for a run down house in an inconvienent area - but if that's what it takes, that what you need to do.
A deal-breaking issue is often whether the dog will be left alone. If you can show that someone will be at home at all times when the dog is there you are in a better position. If you can't be at home, look into dogsitters so that you can show the landlord you have addressed the issue.
You will need to have liability insurance as a matter of course - but be proactive, show the landlord that you have addressed the issue of damage.
If you speak the local language that will be a big plus. If you don't consider hiring a relocation agent who does, who is connected, to advocate for you.
And of course, make sure the rest of your dossier is perfect.
It's not impossible to find housing, thank doG - but you will have to work harder, and likely pay more.
Good luck!