You and your fiancée can submit an application for a
Pre-Marriage Long-Term Visit Pass Assessment. While not a guarantee, a favorable assessment can be helpful.
As background, there are four basic options theoretically available if you wish to move to Singapore with your spouse:
1. Qualify on your own merits (and on the basis of an offer of employment in Singapore) for an Employment Pass, Personalised Employment Pass, EntrePass, S Pass, or Work Permit, as applicable. You mentioned you have concerns about this possibility, although you're free to look for job opportunities in Singapore. A degree is not a strict requirement for any of these passes/permits -- take another look at the Ministry of Manpower's requirements.
2. Singapore Permanent Residency (SPR). This is at least somewhat tough to get when you're newly married but theoretically possible. The government has been approving roughly half of SPR applications from citizen-foreigner married couples at last report. It is possible to lodge an application from overseas via one of Singapore's embassies.
3. Long-Term Visit Pass (LTVP).
4. Long-Term Visit Pass Plus (LTVP+). For both the LTVP and LTVP+ it is generally possible to accept employment in Singapore, but your prospective employer must obtain a Letter of Consent (LoC) from the Ministry of Manpower before you start. The LTVP and LTVP+ are quite similar, but the LTVP+ includes some fairly minor medical care benefits (lower prices at public hospitals and clinics). Generally you need at least three years of marriage or a child together to qualify for the LTVP+.
In all except #1 your wife's income and wealth are taken into account. The government wants to have some assurance that your household will have adequate financial means to take care of itself (and particularly to take care of you, the foreigner in the household).