FWIW, unless you're running out of notes up high (are you playing up above the 12th fret a lot and running out of room?), you'll get more flexibility out of keeping it as BEADG IMHO.
You can get some pretty high notes out of a regular tuning, especially if you have a 24 fret bass.
Having said that, for one or two of the songs I play I really could use a bass that goes a *little* bit higher. But I'd never trade that for the flexibility that the B string gives me. I use the B string constantly.
Also, since you're a beginner, be aware that putting on a high C will change the way you have to approach the instrument. You'll be reaching over that C string all the time. This may or may not be a problem for you, depending on the size of your hands and how good your technique is.
With it tuned BEADG, you can pretty much ignore that B string unless you need it, for transposing songs or playing runs in one position as opposed to heading down the neck to get the low notes.
Just IMHO. If EADGC tuning is your thing, go for it.