no its not too late to register to A-kasse, BUT what is important for you is that you must be sure that you will be able to get unemployment benefits if you get unemployed after your PhD contract ends. Otherwise it gives no meaning to be member of an A-kasse
As a foreigner working in Denmark this means that beyond the normal requirements like danes has to meet:
1. You must have been member at least the last 1 year before apply for benefits.
2. You also must have been working for at least 1 year (=1.924 hours) during the last 3 years. But be aware that only working hours/days from periods where you are member of an A-kasse is counted. See our answer to another question asked.
You do not tell us if you are an EU-citizen or non-EU citizen. Thats important regarding your rights to get unemployment benefits.
If you are an EU-citizen you only have to meet requirement 1 and 2 like danish citizens.
If you are an non-EU citizen then it depends on what you residence permit gives you of rights to work in Denmark.
I assume you have right to work during your contract-period, BUT whats important is that if you apply for unemployment benefits after 31.10.2017, you can only get benefits IF you residence permit gives you right to work FULL time also AFTER 31.10.2017, and you can only get benefits for periods where you have right to work FULL time in Denmark.