That depends on how much tension you like, the density of the strings, and your guitars scale length.

That guitar has a scale length of 25.5", so you can get away with a thinner string than if you went with a les paul, for example.

I wouldn't recommend 9-46 or 10-46 for D Standard, even on a 25.5" scale length guitar and with heavier core strings, you'll feel quite a bit of flub. I would try at least a .11-.48 set like the Ernie Ball Power Slinky, D'Addario also makes a .11-.50 set that I thought were perfect for D Standard.

That being said, maybe you want loose, flubby strings.
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I was afraid of experimenting with the gauge, because I didn't want to damage the fretboard if go with thicker strings. I don't need too much tension and I use a lot the floyd, so the actual question is which gauge will be most friendly to the fretboard (with my aggressive floyd use)? Will the 11's be good decision or there is also other suggestions?
Having heavier gauges of strings will never damage the fretboard.

Just adjust the guitar's setup in accordance to the different tuning and the heavier gauge.

I personally prefer 10-52 for D standard.
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I use 11-56 is D standard. But I like tight strings *shrug*
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11's is what I have used.

Just check and make sure the neck doesn't have too much back-bend, and check the intonation, like is the octave harmonic at the 12th fret or not?

You should be okay, but you'll want to check a day or so later to make sure. Might have to tighten the truss a bit.
I use 10-56 for Drop C and D standard, never had a problem
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I wouldn't use 9s for anything, I hate how those feel. I'm using 10-46 on my standard D and standard E guitars.