I usually do it for about a month. But my tip would be to always have a spare sponge in your filters if possible, this will let you have instantly cycled media if you need it. I have 2 or 3 spare sponges in case of emergencies or quarantines!
Do you have any filter media that you can spare from your main tank to seed the new filter? If so, just don't take so much from the established filter that it causes the tank to go into a mini cycle.
You can use the established media from the old tank or established tank into the new filter. Maybe that's an option for you.
You can also use some of the substrate from the established tank. Place it in a NEVER SEEN SOAP nylon hose (panty hose) and place it in the quarantine tank along with some filter media into the filter.
It's not ideal of course, but you can also do multiple small water changes every day using a product like Prime to try to keep the ammonia down while not shocking the sick fish with larger changes less often.
And in all the stress of caring for a sick fish, don't forget to put some extra filter media in your existing filters for the future.
I'm sorry about your platy but she'll live on in her fry.
What kind of filters do you have? I bought 100% polyester quilting batting which is very thin, less than 1cm when dry and probably no more than 5mm wet, and added strips of that to my filters. Another thing you can do is break a Terra cotta pot into tiny pieces and place those into the leg of brand new panty hose. It's a cheap alternative to those expensive biomax rings.
Sorry she died I have a small filter that runs on an established tank all the time just in case I need to set up another tank fast. that would be some thing you could do now in case you need the "Q" tank in the future.
If your established tank is "heavy loaded" (in terms of bio-load) as opposed to keeping it minimal stocked I think 10 to 14 days will suffice.
On the other hand if you need a tank for quarantine right away, consider removing enough filter media from the main tank and place it in another filter. Replace the removed media if possible (I like using rough ceramic cylinders).
Of course, the type of filter you have may make this harder or easier to accomplish.