I am planning a trip through Russia so I have to get the visa in my own country (Australia). But then I plan to go to Ukraine and I can get a visa upon arrival (if under 15 days). Is there any risk that they would not allow me in? I'm just a tourist although I am of Ukrainian background and have relatives in Ukraine that I will be visiting.
There is no risk. Even Russian citizens are allowed to visit Ukraine, so why would somebody who has visited Russia be not allowed to enter the country?..
Ukraine doesn't practice prohibiting people who have ever visited any other country entrance to its territory.
The only thing you should keep in mind is that if you'll during your visit to Russian Federation enter the occupied territories, such as the Crimean peninsula or part of Donbas behind so-called separation line from the Russian territory, it'll be considered an illegal border crossing and then you'll be either denied entrance to Ukraine or arrested.
You can definitely go to Ukraine after Russia, don't worry.
Note that visa upon arrival only for Australians exists at Ukrainian airports only, and not at the land borders, and that you need to fulfil the requirements for the visa-on-arrival.
Were you to get a visa before arriving to Ukraine, you could cross (to my repeated experience efficiently and hazel-free) overland from Russia. Do, however, stay clear of the Donbass and Crimea to which the dispute has had some profound implications for travellers.