Read all about the "Anthropocene" in
wikipedia. The Anthropocene Working Group (AWG) of the International Union of Geological Sciences (IUGS) has been working (since 2009) on whether or not the Anthropocene should be identified as an Epoch within the Geologic time scale (starting, per the AWG, about 1950). The AWG has said "yes" but the IUGS hasn't adopted the idea. (I have no idea when they will take up the question.) I'll note that all existing epochs have been defined by geological
deposits.
I see this thread's question as more about the current interglacial phase within the larger
Quaternary Ice Age or Glaciation, regardless of whether the term Holocene covers geological deposits made in the future (to be determined by the IUGS).
Antarctica may melt out in as few as 500 years (per
here), but it might not melt completely (if we get our act together). Either way (total melt-out within 5,000 years or not), if we get our act together, thus having learned about controlling climate parameters that will maintain icy poles and a nice (for us) Holocene climate in the mid-latitudes/tropics, this interglacial phase could last a very long time - 10s of thousands of years.
If we totally blow it and go for 10-15C of global warming, Antarctica will melt completely, but I do not have a sense if this will push the Earth into a new climate regime or if nature will take its course, lower atmospheric CO2 concentrations and get us back to Quaternary conditions dominated by Milankovitch cycles.