I was interested today when I found a book on self teaching treble clef for cello and I was thinking... Should I self teach treble clef or should I wait until my tutor decides to go over it with me?

There's absolutely no reason why you couldn't at least familiarise yourself with the book, but you are still a few AB grades away from having to play music written in the treble clef. Until you are familiar and comfortable with playing in high positions (and three octave scales), I wouldn't worry too much.

Familiarising yourself with the note names in the treble clef is probably wise, will make progress later much quicker Maybe worth mentioning to your teacher that you are learning note names, in case there's anything important you should know about it before you start figuring it out for yourself. But I really can't see a reason why you shouldn't look at it.

Thanks for the advice guys, I will ask about it in my lesson on thursday

Just a thought - have you begun reading tenor clef yet? Because if not, it might be more use to familiarise yourself with that first before going onto treble.

I haven't yet been taught the tenor clef, I never thought of that thank you for the suggestion unmusical mum, I guess I should get more familiar 1st with tenor and then move on to treble clef at a later date

Thank you everyone for all your suggestions, you are all stars

I'd advise learning some tenor clef first, as you come to that in pieces much sooner than treble clef.... It'll be much more useful in your immediate future.