I'm assuming that you're bringing it in at night because it's cold?
You will need to wait until there is no chance of heavy frost before you plant it outside. Normally raspberries can tolerate cold as dormant canes. (Mine are still dormant.) But once they've leafed out like yours, it may hurt the plant to plant it outside when it's freezing over night by a lot.
As long as you're putting it out everyday you're "hardening it off" which is good. It's adapting to the heavy UV light from the sun. Stores don't produce the heavy UV.
I'm not certain about the drooping though.
I'm guessing that it may be root bound.
Which means it'll do a lot better once you're able to plant it outside.
OMG. I first started writing thinking you were in Idaho!! (Zone 6a)
If you're in Nevada I would put in the ground ASAP.
If it is root bound, tease out the roots a little so that it gets a better kick start.
My raspberries often droop during the day when it's very hot.
Do they come back at night when it's cooler?
I am way behind you! Mine are still just bare canes.
