As Ashley says, 'yoghurt' is the standard spelling in Britain, while 'yogurt' is standard in North America.
'Yoghourt' is not wrong, however: it's just very rare nowadays. Ashley looks quite young, which explains why she has never seen this alternative spelling and presumes that it must be incorrect.
In fact, when yoghurt first caught on in English-speaking countries, in around the 1960s, all three spellings were used: yoghurt, yogurt AND yoghourt, along with several experimental pronunciations. As the product became a staple, we settled on fixed spellings and pronunciations: usually 'yoghurt' (pronounced like "yoggut") in the UK and yogurt (pronounced like "yoe-gurt") in North America. Australia, meanwhile, uses the British spelling but the American pronunciation, as far as I know.
I hope that helps.