You need certificate of permanent residence (after 5 years in Finland) in order to live and work elsewhere in EEA (except in UK, Ireland and Denmark). So to work in Malta, your EEA partner needs to be a qualified person there, exercising treaty rights in Malta. You can enter Malta with your partner on your residence card, but in order to live and work, you need to apply for residence card with evidence of your partner's qualified status, such as working in Malta.
Between have you got any clue how long it takes before you get the residence card in Malta or it works like UK system that you get Certificate of Application which can be used for job hunt while waiting for the residence card. We are about to move to Malta as my partner just got job offered and I don't wanna stay too long without work.
Also do you know how long the first Maltese residence card for?