Shoot, honey, isn't that kind of like asking, "How old do I have to be before it's reasonable to tackle riding a bike?"
IMO, if you're old enough to be asking the question, then you're old enough to at least try. Bolt the training wheels on and go for it.
I dunno, I don't "get" people who think there's some sort of arbitrary cutoff somewhere that says whether you're "qualified" to try to learn a piece. I say, if a piece interests you, then hey, go for it. If it turns out to be too hard, then just stick it back in the piano bench and come back to it later.
Also, I think it's important to realize that a piece doesn't have to be learned concert-hall perfect. It's okay to mosey your way through it at half-speed as long as you're happy.
To me, that's the important thing--be happy. Have fun. If it isn't fun, don't do it.
From a practical standpoint...
Well, I'm printing it out from sheetmusicarchive right now, both Arabesque 1 and 2 (BTW, thanks for the pointer, I had actually never heard of them, but they look interesting and do-able), and...
...hey, I could play them. No. 1 is just basically all arpeggios, five pages of arpeggios. Granted, they're not "Haydn" type arpeggios, they're "Debussy" type arpeggios, so they're not going to form big thumping dominant-to-tonic chord progressions, so it'll be tricky to tell whether you're playing the right note, but that's all it is. No Rachmaninoff World-Devouring "But I Can't REACH A 14th!!" Chords. No 18th Century "Are We There Yet?" eighth-note runs.
No 16th notes in No. 1; No. 2 has 16th note triplets, but once you get the rhythm right ("mother-in-law, mother-in-law") they shouldn't be a problem.
No. 1 is in the key of E which might be a little intimidating at first, but not after you get used to it.
No. 1 has a few accidentals, not a problem...hmmm...No. 2 has a lot more, but...it's important not to be afraid of accidentals. Once you get them into your fingers you won't even notice them as they go past.
Oh, and my level of expertise?
...I'm halfway through the John Thompson Fourth Grade Book.
I can play these. So can you.
P.S. Get an edition that has fingering; this public domain one doesn't.