I grew up with this condition and majored in neuropsychology, and cannot emphasize enough that for your daughter's sake you *must* consult a pediatric ophthalmologist ASAP so as to definitively ascertain the underlying cause of your daughter's amblyopia.
In my case, the cause was a congenital cataract, and thus was uncorrectable within the critical period window (~6 years) using the medical procedures of the day (the early 70s) without what my parents considered unacceptable restrictions on my activity. Today, surgically removing a congenital cataract is an outpatient procedure.
There are other possible causes of amblyopia ranging from neurological to muscular, and almost all of them are entirely correctable if identified at an early-enough age. Some are even correctable without surgery. For example, Botox was originally invented precisely to non-surgically correct some types of amblyopia; its repurposing as a general cosmetic came much later.
In my case, even though the problem wasn't correctable the doctor prescribed an eye patch so that the lazy eye could develop as much vision as physically possible, and he asked my mom to have me wear it for a certain number of hours a day (I believe 2, but can't say for sure).
My mom reports that she did her best to turn it into a game, but that wearing the patch would change me from an energetic, irrepressible 4-year-old into a despondent, pouty child, and it nearly broke her heart to have to do it.
Most importantly, she had to constantly interact with me the whole time the patch was on to ensure I wore it for the prescribed daily period. One trick she discovered was to spend some of the time "watching TV" with me (though not much because I was allowed very little TV time as a child). Of course I couldn't really see what was happening on the tube, but apparently I thought the random flashing blobs of color were cool, and so she would have me make up stories about what I thought I was seeing.
Flashing forward, even though the underlying problem couldn't be fixed, in the long run it was worthwhile to patch the eye because not all vision is lost even with something as severe as a cataract. Instead, in my particular case the peripheral vision in the eye was strengthened to the extent that today it can nearly-normally detect motion as well as detecting larger objects based upon color and (longer) edge cues.
Furthermore - for the many years before I got the eye Botoxed last year to appear normal to casual inspection - I had a 175-degree field-of-view (most people have around 150-degrees), with my brain stitching the signal from my left eye together with the peripheral vision from my right eye to create a seemingly continuous peripheral visual field to my left. This gave me a "special skill" while driving: I never had to look over my left shoulder to change lanes to the left because slightly angling my head to the left would reveal any cars in the lane next to me.
Point being: even in the worst case scenario where the problem can't be fixed, the brain will adapt to create the best outcome *if* the eyepatch is worn faithfully as a child.
Additionally, Botox can usually sufficiently-fix the cosmetics of a wandering eye in an adult, though I definitely would *not* recommend using it purely for *cosmetic* purposes on a child. Rather, IMO (which you're welcome to disagree with of course) Botox should only be used on a child if the expected outcome is that its use will result in normal binocular vision development.
Finally, current science is in the process of discovering that the end of the critical period for developing normal binocular vision may not mean that an adult's amblyopia can't be fixed. There was a good article in Scientific American about 6 months ago describing video training software that is being developed for the purpose, and that has met with unexpected success for some types of amblyopia. All of which is to say that if the problem can't be fixed within the critical period, there's still hope that in a few years the science will be at the point that the end of the critical period will not matter for much.