At what age is it safe for a toddler to climb stairs alone?

C

Our master bedroom is upstairs, and our daughters (age 1 and 3) are both downstairs.

The 1 year old sleeps well and hasn't mastered door handles yet anyway so isn't an issue. But the 3 year old will wake up during the night and immediately come looking for us.

We've explained that she doesn't need to do this, that we have the monitor and all she needs to do is call for us and we'll come to her, but she's not interested.

We have a gate at the bottom of the stairs for obvious reasons. And we don't feel comfortable with her going up the stairs at night, half asleep, unsupervised. So when it's time for my husband and I to go to bed, one of us will go in with her - just to avoid this situation arising. I'm tired of it but we just haven't come up with an alternative solution.

Are we being OTT? Should we just let her climb the stairs to find us? Should we leave the gate shut and have her yell out for us and risk waking her baby sister and just deal with it? Would love to get some advice and opinions!