It must be totally doable, the crossing itself is only 15km. I haven't done it but am myself thinking of longdistance sailing on my FxOne.
You should study tidetables or get local information as the current through the strait can reach 5 knots
Watch out for heavy traffic going through the strait and ferries from Spain to Morocco.
You will have to prepare standard papers for yachts with crewlist for clearing customs and you must find out in which harbour you can do the clearing.
In Denmark a longdistance yachting club can help with these papers, maybe there's one like that in Portugal
The atlantic has been crossed on a hobie in 15 days and the Mediterranean in 54 hours. Hobies are FAAAST

Check out the video
http://www.defi-terresens.com/multimediaLets hear your experience and see photos from the trip and the equipment
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Poul
FxOne 165

I'd Rather Regret The Things I Did, Than The Things I Didn't