Marrying a Czech citizen

My financee and I are planning on returning to her homeland in March from the UK where we both work right now.

I'm an Australian citizen and she is Czech.

My question really centres around what happens after we are married in regards to residence.

Will I be afforded the same rights as a Czech citizen ie: free to travel the EU countries and work (we both want to travel and work); Welfare payment (in case I have trouble finding english teaching work while in CZ). Also how long does it take from the date of marriage for one to obtain residency?

It's a little difficult to find the info I'm looking for, so if anyone has been in a similar situation or knows the answers to my question, it would be great if you could leave some info,

Cheers!