Is she actually entered for a summer session exam? If it's ABRSM the entry deadline was the end of April, so it's too late to be starting to think about doing it now.
I'd say only grade 7/8 anyone would really pay any attention to higher grade passes, and only then if the DC was quite serious about their music and aiming for A-level and beyond in their musical journey.
For grade 2, no one is going to be asking next year, in 5 years or in 20 years, did she get a pass, merit or distinction.
I wonder if the teacher didn't enter her and is now trying to persuade you it would be in your daughter's best interest to take it in the autumn, even though she's ready now to cover their error of not making the entry.
Will your DC get bored playing the same pieces for another 4-5 months? Personally if they can pass it now, and there is an option to do it now, I'd just get it over and done with and move on to some new fun music for the summer.
If it's not ABRSM, or not an exam with an entry deadline, please ignore my post, other boards may well hate different entry criteria