Yes, your regular expression is correct, language defined by the NFA in picture either accepts null string ^ or (aaa)+ or (bbb)+. You have covered ^ in * closure.
If you wants you can make its DFA something like as below:
__ bbb __ aaa
|| ||
▼| ▼|
--►((Q0))---aaa---►((Q1))
Where both Q0 and Q1 are final states (Q0 is start state).
side note: you can replace edge labels of 'aaa' to 'bbb' and 'bbb' to 'aaa' to get another form of same DFA. Additionally, in standard form of DFA an edge lable can be single language symbol.