We had an almost identical situation, OP.
My husband is now my ex-husband.
This isn't about the wardrobe. It's about your DD and her father not respecting her but controlling her and stunting her growth. He wants to inhibit her. It sounds crazy and 'out there', I know. And it sounds like I'm overthinking this. But believe me, I lived out this scenario for years. The bedroom that our DD could not move into became the elephant in the room and there was so much psychology attached to that; so much so, that it became a huge focus with my DD's CAMHS therapist. In my own case, my marriage ended for sinister and sad reasons. My ex-husband had been abusing our daughter. This is not at all what I am saying is happening here. But you do have a 'control thing' going on. Yes, the wardrobe's a bit of a hassle, but it's not the reason she can't move into that room. It's your husband's shitty excuse. He's probably not even aware of his antics, but he's holding your DD back. She's at such a crucial age too.
And you have the room! Why wouldn't you move her? It's totally logical that she'd move into that bigger room. Why else do we have family homes?
I was so angry when my DD, who'd been sharing a room with her little brother for years, was trying to deal with periods and pads and puberty in a bedroom that wasn't her private space. I used to argue my daughter's case to no avail.
On the day I finally went to deal with it and tackle the spare room, my ex, while I went out for a few hours, filled up the spare room with the contents of the loft with the excuse that it was easier for us to access shit we hadn't accessed since dinosaurs roamed the earth! I mean, things are stored in the loft for a reason: So that we don't ever have to access them!
We also had two bookcases in the spare room. They were my ex's initial reason for not allowing DD to move into the room. Let me tell you about these shitty bookcases. They were ancient IKEA ones (nowt wrong with that, however...) that came with the house years and years ago. The previous owners had left them behind. They were falling apart. When I tried to dismantle them years ago, my ex came upstairs, shouting at me. He went into a rage. And that's when he turned the spare room into our 'external loft'.
This summer, I hired two guys to come upstairs and help clear out the 'external loft' that my ex 'created'. It was ecstasy listening to those two guys dismantle the bookcases. They had to smash them up. When they threw them into the back of their removal truck, the pieces kept hitting the keys of an old, tinny, out-of-tune piano that was in the back. It was the sweetest music to my ears.
I say throw the husband out with the bloody wardrobe!
In all honesty, this is a bit of a crossing the Rubicon moment for you, OP.
This is more symbolic and psychological than you think. Your husband is holding his daughter back and yes, wasting useful space (mine was excellent at wasting space). When the wardrobe's needs are greater than his own DD's, you've got to look at the man himself. Be bold. I say dismantle that mother fucker and don't even shy away from his reaction. Be strong. Do it! Claim that space and do this for your DD. It will give her a good, positive, loving message too! She's being bullied by her father.