Depending on how well the area is sealed/insulated, and how many BTU's it puts out, it might work, but it will just add more wear and tear on your compressor. Heat pumps, for the most part, work well as a supplement to another heating system. Larger units do exist, and some will swear by them, but there are far cheaper and more efficient sources out there. If you have natural gas available forget the heat pump immediately. Maybe snoop around for a used forced air or hydronic furnace? I've seen quite a few nice AC units, minisplits, furnaces, etc all under $1000 in very good shape.
As far as design goes, you didn't say whether or not the room would be sealed but I'll assume it isn't. If space permits, look into making a lung room, that way you can do as you wish with air thats the temp you want. Sky is the limit from there, just size your equipment and ducting properly. You could even utilize it for fresh outside air exchanges with out spending big $$ on an air handler type unit, like timing a fresh air intake to fill the room for 5 minutes every hour while dampers shut on the supply and return, closing intake damper then circulating that fresh air through the rooms and back through the "lung room" through a return system to keep it at a set point. Lots of different ways to make it work from there.
