EU Pet Passport - UK to France

Hi all - first post for a new member. 

We have just welcomed a new 4-legged member of the family from Romania (Dee) who has an EU Passport. We're planning on taking the motorhome (Toleno L) to France in September. We want to keep the EU Passport live therefore I believe any vaccines or boosters require to be undertaken in the EU. 

On the Sunday we are due to return her rabies vaccine expires so intending on obtaining both tapeworm treatment and rabies booster at the same time. 

Am I right in saying that: 

a) If its a first vaccination or vaccination as previous one has expired I'd need to wait 21 days following vaccination until I returned to UK

b) if its a booster to a vaccination that has not yet expired we will be able to travel immediately

c) As long as EU Pet Passport vaccinations etc. and info is up to date I won't have any requirements on leaving UK  

Thanks all - and happy motor-homing! 

Stuart