Yes at the moment living with you I don't think she'll be getting any housing benefit. Sounds like you're getting the HB for a 2 bed but living in a 3 bed.
Or maybe she's too old to be considered a dependent and you're only getting the 1 bed rate? And she's currently getting the shared accommodation rate?
If nobody is currently getting any HB for DD then get her a lodger agreement for your home ie you're renting a room to her, it's nothing to do with your landlord, look online for a template document. Then she can claim HB costs in her UC, make the rent whatever the maximum shared accommodation rate is.
If she moved out you'll both get the 1 bed rate once she's over 35 or claiming PIP.
As you're in private rental get yourself on the social housing register too. Even if it takes 20 years for you to get a place. The rents don't exceed the full HB rate. Unless your property is bigger than you're assessed as needing, so you'd get a 1 bed rate as a single person even if you lived in a 2 bed, but even then the extra you'd have to pay would be around £50/pcm. If all you're going to have is a state pension you need social housing.
Get DD on the register too. Even if she's not going to bid for anything yet (don't mention this). One of the factors in allocation is time waiting. The sooner she's on the register the better.
What do you want to do, live separately or together? If there's a shortage of 1 bed property in your area, you might have better luck securing a 2 bed and you'd have higher priority for that if both bedrooms were going to be occupied. If it doesn't work out and DD subsequently gets a place of her own, all that changes is her HB would no longer cover half your rent and you'd drop to the 1 bed rate needing to pay the extra yourself or look to downsize.
Once you've applied to the housing register it's not set in stone. If circumstances change, eg evicted from current house or you develop medical conditions, you update your application and they recalculate your entitlement to a property and your priority status.
Claim PIP now, it goes on inability to do things not her diagnosis, although diagnosis helps.