Most caravan parks will tolerate small dogs kept on leash and cleaned up after "Whoopsies". Ensure your dogs are fully vaccinated and take copies of certifications with you - Ensure dogs are ear chipped and wearing ID collars at all times. Also be aware that many areas have 10-80 baits spread around (normally signposted but not always).
When you want to go into areas that don't permit dogs you will normally find someone (like me) that will mind them for you for a day.

We travel with a small fur baby she is always on a lead and always pick up after her .We always manage to get her either in day care or the vet normally do day care .As Possum said a lot of the times we have looked after some body's dog one day.and they looked after ours the next ,just to help each other out ,It is not the end of the world travelling with a fur baby you just work round it, hopefully you will do it. Trevor

We travel with our dog we stay at showgrounds or recreational grounds they are pet friendly have power showers toilets water and also dump points much cheaper than caravan parks and have plenty of room for your furbies

We have travelled with small dogs for many years. Never had a problem finding somewhere to stay. However there are limitations. A lot of tourist attractions are not dog friendly but many are. We are planning to do Tassie with friends in 2019 and we will get a housesitter for the 6 weeks. We dont want to miss anything down there as it will probably be a once only trip and there is just too much to see. Not looking forward to leaving him but just once wont hurt him. He has been through Qld and Victoria and will definitely do the big lap with us when hubby retires.

As others have said there are a few limitations on access and admissions, but as dog lovers we happily accept that. If you download the Wikicamps app you can filter out non-dog friendly caravan parks, we use it for planning all the time and it saves you wondering or making endless phone calls. I'd estimate that about 75% of parks are dog friendly, slightly less so in coastal areas. Travelling off season has added benefits when some of the usually non-dog friendly parks will occasionally relent, plus you encounter fewer if any noisy kids!!