Props Ideas for Crafting a Sickroom?

What's your budget? The set is available on eBay for under $100, but it's definitely bumped up.

 

Interesting project! Are you making the bedside table etc from scratch? How durable do the furniture need to be would affect the materials, I was wondering what you're planning and comfortable working with, cardboard, wood, air dry clay...?
For the adjustable bed is the "folding mattress" / raised pillow end the important part or do you care about lifting and lowering the bed? Maybe some wire and cardboard could be used to keep the pillow end propped up when needed. Or you might imitate something from book stands or those tablet covers that work as a stand to keep a small screen up.
Since dolls are so small for the tubes (IV and such) if you can't find tiny enough vinyl tubing maybe a clear fishing line could work?
For the IV bag is there suitable looking ice cube freezing bags available? I don't know if there are different sizes but if there was something close enough you could just cut out one ice pocket to work as the bag. You could fill it with clear glue or something else that dries not-runny, perhaps if it's held compressed as it dries you can make it look thinner or thicker as you like.
Anyway good luck and I hope to see/hear how it goes!

 

For items like oxygen tanks, you could try air dry or polymer clay depending on size. There might also be plastic model kits you could look into that might have really detailed pieces for a sick room for a good price.
As for an adjustable bed, depending on the brand/type bed you are going for, perhaps thick wire to hold it in place as it moves, or maybe a gear that could be wound up?
As for the oxygen mask, clear epoxy resin or maybe a small amount of vinyl fabric with clear plastic on the rims to hold it up?
Good luck on your project! It seems like it'll be really interesting!

 

I just checked Target with the link you included and it says the set is in-stock for shipping, at least for my location (Michigan, USA). Might be worth another look!