It is really important to get a child assessed early if they are having issues with learning. If you don't get an assessment done and down the road you do find out there is something, think of all the years in between that your child has struggled.
Getting an assessment done does "not" mean your child is dumb or not intelligent, it simply finds out the areas they are having issues with, what the reason behind it is, and once that is figured out then the team and you can go ahead and form a plan (IEP).
Learning Disabilities are not abnormal, most people with LD's are average to above average intelligence. It just means they learn different.
With an IEP in place, it will set up guidelines as to how your child is tested, taught, recommendations etc. The school has to follow this and you have input into it as well. That way if there is an issue, your child will be taught in the correct way, not having pressures put upon her that are unfair, causing her to lose interest in school, and school work.
As for being graded a grade level below, that is fine as long as she is progressing. And maybe once you find out if there is an underlying issue (learning disability, etc) then you and the school will know which way to proceed with teaching and testing. You may find she catches up or comes close.
Tutoring helps, but if there is a learning disability, the tutor will not know how to teach in the correct way, or if you find with the tutoring she is still struggling then something else need to be done.
I have been here, had our son assessed just before grade 2 due to reading issues. Turns out he is average to above average intelligence, above average in writing when given a guideline but has a working memory issue, therefore a learning disability.
I will never regret having him assessed, and urge parents to put their fears aside that something could be wrong, when in fact if there is, doing something is better than nothing and giving the child the happiness they deserve in school without the extra struggles/pressures. Hope this helps.