Managing an international database,etc

I am quite a novice when it comes to networking and hosting
packages. My company at the moment has the main base in
Australia and this is where the company database on filemaker is
kept on all clients and company financials. We now have branches
in the UK and Europe and we access our database via timbucto
which is slow and not always accessible. Is it possible to host these
programs on a central server and allow staff to enter and update
the database directly and quickly?