Could I bike up this?

My SO sent me a picture last night of this mountain pass, which is near to the hotel that we're staying at in the Italian Alps while on vacation this summer. He's thinking about biking up it (which I have no doubt he could), but crazily enough I'm thinking about biking up it, too.

If we started right at the base of the pass the trip wouldn't be all that long distance wise (about 25km), but of course since it's a mountain pass it is quite a bit up (1800m or so). That makes it substantially more climbing than anything I've tried to to before in one day, but maybe with the short distance and taking it slow I could spin my way up this thing.

One of the things that I love about biking is that I feel so thrilled every time I reach another small milestone that I've set for myself. I've never been an especially athletic person, and biking is one of the few activities that makes me feel proud of my physical abilities (as opposed to intellectual or whatnot). I already have a few new biking goals in mind for myself, one of which will be to try a metric century sometime this summer, which I'm pretty sure I could do as long as it was a fairly flat route. Should climbing this mountain pass be another? I'm pretty sure I'll hate myself halfway up the mountain for doing it, but I'm also pretty sure I'll feel amazing if I make it to the top.