The two of you can stay together in Sweden for up to three months, without regard to your ability to support yourselves. To stay longer, you will need to apply for a residence card. If she does not have a job by the end of the three months, you can apply for the residence card on the basis of self sufficience. The minimum amount you need to show will depend on how long you intend to stay, but it cannot be greater than the minimum wage. An overseas account should be fine. Details are available at https://www.migrationsverket.se/English/Private-individuals/EU-citizens-and-long-term-residents/Work-study-or-live-in-Sweden-for-EU-citizens/Residence-cards-for-family-who-are-non-EEA-citizens.html
The Swedish government pages do not make it easy to find out when one must apply for the residence card, but the European Union directive, 2004/38/EC, is quite clear: the deadline for submitting the application may not be sooner than three months. Furthermore, there may not be any conditions imposed during the first three months other than a requirement to hold a passport and, depending on your nationality, a visa for entry.
Article 6:
- Union citizens shall have the right of residence on the territory of another Member State for a period of up to three months without any conditions or any formalities other than the requirement to hold a valid identity card or passport.
- The provisions of paragraph 1 shall also apply to family members in possession of a valid passport who are not nationals of a Member State, accompanying or joining the Union citizen.
Article 7 covers the right of residence for more than three months. Article 8 concerns administrative formalities for union citizens, and article 9 concerns administrative formalities for third-country family members:
Member States shall issue a residence card to family members of a Union citizen who are not nationals of a Member State, where the planned period of residence is for more than three months.
The deadline for submitting the residence card application may not be less than three months from the date of arrival.
Failure to comply with the requirement to apply for a residence card may make the person concerned liable to proportionate and non-discriminatory sanctions.
Regarding travel to an EU country without having a job, for the purpose of looking for work, see article 14(4):
- By way of derogation from paragraphs 1 and 2 and without prejudice to the provisions of Chapter VI, an expulsion measure may in no case be adopted against Union citizens or their family members if:
(a) [omitted because it is not relevant to this answer]
(b) the Union citizens entered the territory of the host Member State in order to seek employment. In this case, the Union citizens and their family members may not be expelled for as long as the Union citizens can provide evidence that they are continuing to seek employment and that they have a genuine chance of being engaged.