No. If the prescription is as you say, waiting 1 or 4 weeks for a second
opinion is NOT likely to cause any problem

Again, nothing in your description calls for treatment at that age.

-MT, OD

Neither getting the glasses nor skipping the glasses will do any harm
to her vision, period.  If you see someone named Otis posting, ignore
him.  He's a kook who thinks wearing glasses will make your vision
worse (it won't).

I'm no optometrist, so take this as only the interpretation of someone
who's worn glasses/contacts for over 20 years.

-0.25 -0.50 x 180 written twice seems to suggest this:

For each eye, -0.25 diopters spherical correction (meaning she's very
slightly near-sighted - contact lenses are only manufactured in 0.25
diopter steps, to give you an idea how slight that is).  Also for each
eye, -0.50 diopters of correction for astigmatism (making the lens
somewhat more like a cylinder than a sphere), at an angle of 180
degrees.

The only way this can fit with a comment about one eye being weaker
than the other is if she also shows a difference in accomodation
ability.  That is, she can focus properly on an object at a shorter
distance with one eye than the other, with the one that requires the
object to be further away being the "weak" one.  There's nothing in
that prescription to correct for this.

I can't even think of an activity for a 3-year-old where the clearest
vision possible is critical.  In your position, I would not fill the
prescription.  I'd wait until she was at least in school and had to
read a blackboard before deciding if she needs any correction or not.
With those numbers, she's not suffering any great loss of visual
acuity.