You should be able to pickup filemaker easily with your background. FileMaker is more expensive to use than databases like foxpro. FileMaker requires a copy of filemaker on each machine connecting to the databases unless they connect through Instant Web Publishing or FileMaker GO. Go is for the iPad / iPhone. FileMaker is not really like Foxpro or .Net but is very easy to learn. You can download a trail version of Filemaker to take a look.
You can make your own plugin and there are several plugins available which you may need for the Quickbook connection. FileMaker Has export functions.
The expense could run high depending on the number of users.
Quickbooks connectivity is possible with a plugin http://www.fmbooksconnector.com/ $200 single user - windows only
I've done some reading on FileMaker and some "experts" say it is too restrictive in what you can do compared to other development systems.
Is this biased, bad or old information?
Few programs are without limitations, gotchas, and work arounds.
There is a long and informative thread on the FMP Tech Network started by a long term FMP developer fed up with the limitations.
This is a blog post about it. http://filemakeraddict.blogspot.com/2012/08/hello-filemaker.html
and some "experts" say it is too restrictive in what you can do compared to other development systems.
I've compared FileMaker to how development works in other systems like this:
Developing in FileMaker is like constructing a building with modular prefabricated "snap together" components, while developing in many other systems is like constructing the same building out of individual boards and nails. Because of this, your "construction costs"--the time spent paying a consultant to create the database for you is very low for FileMaker as compared for many other systems. In fact, "non-experts" are often able to create their own database without having to pay a consultant to do it at all and even for us programmers the time it takes to go from concept to reality can be much shorter.
But that same "modular construction" can also be a negative. If the client wants some specific feature for which FileMaker does not have a component ready to go, creating that capability may be anywhere from difficult to impossible where the other systems and their "boards and nails" components may be able to construct it quite readily. I encounter such issues with FileMaker pretty rarely, however, as it has a fairly complete feature set.
Many "experts" who don't actually make regular use of FileMaker as also hindered by a "SQL" mindset. Since they are familiar with the way an SQL query functions, they often have to search for a non SQL alternative in Filemaker to do the same thing and this can generate some frustration for them, where a "newbie" without that need to "retrain" often takes to FileMaker with enthusiasm finding it quite easy to use to develop the solution that they need.