I enjoy this board immensely for the opportunity it gives me to hear from people so much more informed than myself.
However, I have noticed that people seem to speak of "Montessori" schools with no distinction made as to whether the school is AMI, AMS, or not credentialed at all. This makes a HUGE difference. I have visited Montessori schools that are probably safe daycare environments, but I wouldn't rely on them to educate my dog.
In the US, most good Montessori schools start at age 3. Some do have programs for younger children, but it's rare. I think in Europe it's more common to have something called a creche for younger children. I don't know anything about that.
The most typical Montessori classroom is children ages 3-6 and the traditional curriculum covers 3-12, grouped 3-6 and 6-12. I think it is important to point this out, as your child will not be 3.
My children have attended three Montessori schools and I have toured and considered four others. In my experience the AMI schools (I've seen two) are excellent. The AMS schools are mixed (I've seen two - excellent and mediocre) and the non-credentialed schools (I've seen three) are not very good. I would much rather send my kids to a high quality non-Montessori school, than a school that uses the label but has untrained teachers and a mish-mosh of the Montessori materials.
So if you haven't already, I would advise you to research the Montessori schools with this in mind.
If you move in January, couldn't you sign up for the daycare for January - summer and then re-evaluate for fall? If your daughter turns 2 in January she will not be that close to the upper age limit at the daycare.
Also - don't forget to consider the value of your convenience. If your commute to daycare is shorter, that's more quality time with your daughter. If the daycare has longer hours, that's less stress for the family if you have a project to finish with a deadline on occasion.
I guess my main point is that your daughter is not old enough for school. Just because something is called a "school" doesn't make it superior to a high quality daycare populated by professors' children.
Unfortunately, as far as I can tell the Montessori schools don't have any sort of accreditation there and are not associated with any particular group so it's really hard to tell...
The daycare idea is what we're thinking of at the moment because it would buy us some time in this regards but it also has the problem that if it's a bad fit we'll be stuck with it for half a year.

What we've been seeing from the schools is that many will pick up your kid from your house and take your child to school. The daycare does that too. Although the daycare is the closest and we're not sure if we want to use the pick up option...